NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives Ex 13.1
Page No 301:
Question 1:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4863/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m595fd026.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4863/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m595fd026.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4863/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_4ed8a77f.gif)
Question 2:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5630/Chapter%2013%20Math_html_7b495a5d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5630/Chapter%2013%20Math_html_7b495a5d.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5630/Chapter%2013%20Math_html_m72d8ad7f.gif)
Question 3:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4865/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_mb70479b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4865/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_mb70479b.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4865/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m31f790f0.gif)
Question 4:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4866/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m7e193dae.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4866/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m7e193dae.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4866/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_844cdd1.gif)
Question 5:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4867/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1cb8f0c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4867/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1cb8f0c4.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4867/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m24e1ea68.gif)
Question 6:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4868/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6124b4a9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4868/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6124b4a9.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4868/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6124b4a9.gif)
Put x + 1 = y so that y → 1 as x → 0.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4868/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m588af99a.gif)
Question 7:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4869/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_421d3b19.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4869/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_421d3b19.gif)
Answer:
At x = 2, the value of the given rational function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4869/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4869/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_39991e61.gif)
Question 8:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4870/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_6a0c3090.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4870/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_6a0c3090.gif)
Answer:
At x = 2, the value of the given rational function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4870/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4870/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_60df8a2b.gif)
Question 9:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4871/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1cccad73.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4871/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1cccad73.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4871/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_76075cac.gif)
Question 10:
Evaluate the Given limit: ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m28187a9c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m28187a9c.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m28187a9c.gif)
At z = 1, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
Put
so that z →1 as x → 1.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m43c5756d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4872/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m18ead9a3.gif)
Question 11:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4873/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m5c15f2dd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4873/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m5c15f2dd.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4873/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m55a88986.gif)
Question 12:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4874/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m23162328.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4874/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m23162328.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4874/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m23162328.gif)
At x = –2, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4874/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4874/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m37524da.gif)
Question 13:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4875/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3002969c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4875/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3002969c.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4875/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3002969c.gif)
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4875/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4875/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m2c4b5a66.gif)
Question 14:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4876/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m707e4d3b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4876/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m707e4d3b.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4876/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m707e4d3b.gif)
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4876/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4876/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_2060ce88.gif)
Page No 302:
Question 15:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5631/Chapter%2013%20Math_html_2e449afb.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5631/Chapter%2013%20Math_html_2e449afb.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5631/Chapter%2013%20Math_html_2e449afb.gif)
It is seen that x → π ⇒ (π – x) → 0
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5631/Chapter%2013%20Math_html_aab0d7.gif)
Question 16:
Evaluate the given limit: ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4878/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3f163715.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4878/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3f163715.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4878/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m27ee139e.gif)
Question 17:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4879/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m69a98606.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4879/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m69a98606.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4879/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m69a98606.gif)
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4879/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
Now,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4879/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_68132f85.gif)
Question 18:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4880/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_78712a19.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4880/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_78712a19.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4880/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_78712a19.gif)
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4880/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
Now,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4880/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_40ae4546.gif)
Question 19:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4881/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m141e460d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4881/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m141e460d.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4881/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_2af32bf0.gif)
Question 20:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4882/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m22975e89.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4882/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m22975e89.gif)
Answer:
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4882/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6775a6f1.gif)
Now,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4882/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_4a7b1ec2.gif)
Question 21:
Evaluate the Given limit:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4883/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_5c785e49.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4883/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_5c785e49.gif)
Answer:
At x = 0, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4883/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_431d519a.gif)
Now,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4883/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_1f095b14.gif)
Question 22:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_m73ce9ddf.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_m73ce9ddf.gif)
At
, the value of the given function takes the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_m3b802b84.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_m6775a6f1.gif)
Now, put
so that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_6c5038d4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_8cd93dd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5632/Chapter%2013%20Math_html_1ccfff30.gif)
Question 23:
Find
f(x) and
f(x), where f(x) =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_21af3567.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_61e94ed0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m26b4def2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_21af3567.gif)
Answer:
The given function is
f(x) =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_21af3567.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_21af3567.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_70a5c6d6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_5f692eda.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m3cf0e812.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_4a3657aa.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4885/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_1af6170b.gif)
Question 24:
Find
f(x), where f(x) =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4886/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_656f40fb.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4886/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m26b4def2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4886/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_656f40fb.gif)
Answer:
The given function is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4886/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_40ab75bd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4886/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3c44e10c.gif)
Question 25:
Evaluate
f(x), where f(x) = ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m30038629.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_61e94ed0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m30038629.gif)
Answer:
The given function is
f(x) = ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m30038629.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m30038629.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3826da52.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4887/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6cbf9b37.gif)
Question 26:
Find
f(x), where f(x) =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4888/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_4b623cc0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4888/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_61e94ed0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4888/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_4b623cc0.gif)
Answer:
The given function is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4888/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1db76ee1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4888/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_48cc43f0.gif)
Question 27:
Find
f(x), where f(x) =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4889/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6f7dcf6a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4889/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_412b0631.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4889/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6f7dcf6a.gif)
Answer:
The given function is f(x) =
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4889/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6f7dcf6a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4889/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m57e632c4.gif)
Question 28:
Suppose f(x) =
and if
f(x) = f(1) what are possible values of a and b?
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4890/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1dcb780b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4890/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m26b4def2.gif)
Answer:
The given function is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4890/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_78419751.gif)
Thus, the respective possible values of a and b are 0 and 4.
Page No 303:
Question 29:
Let
be fixed real numbers and define a function
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m46bf2da0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_59756b35.gif)
What is
f(x)? For some
compute
f(x).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m7020fe52.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m6ab24595.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m45d00c5f.gif)
Answer:
The given function is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_59756b35.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4891/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_a520fbe.gif)
Question 30:
If f(x) =
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m209beae2.gif)
For what value (s) of a does
f(x) exists?
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m45d00c5f.gif)
Answer:
The given function is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_mbe6370.gif)
When a < 0,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_596cd142.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m7726b6b1.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_65517429.gif)
When a > 0
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m83a3511.gif)
Thus,
exists for all a ≠ 0.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4892/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_3ea73ae5.gif)
Question 31:
If the function f(x) satisfies
, evaluate
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5633/Chapter%2013%20Math_html_3afb4c99.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5633/Chapter%2013%20Math_html_77bb2492.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/5633/Chapter%2013%20Math_html_m6b378f80.gif)
Question 32:
If
. For what integers m and n does
and
exist?
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m48ad236.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1edb5ff8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_1a4562d5.gif)
Answer:
The given function is
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m48ad236.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m10cab000.gif)
Thus,
exists if m = n.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_m1edb5ff8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_2eac5caa.gif)
Thus,
exists for any integral value of m and n.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/173/4894/NCERT_16-10-08_Khushboo_11_Math_Ex-13.1_32_SU_SNK_html_1a4562d5.gif)