rd sharma solutions for class 11 maths chapter 29 limits
TRANSCRIPT
![Page 1: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/1.jpg)
RD Sharma Solutions for Class 11 Maths Chapter 29 Limits
1. Show that does not exist.
Solution:
Solution: Aakas
h Ins
titute
![Page 2: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/2.jpg)
So, let x = 2 – h, where h = 0
Substituting the value of x, we get
Aakas
h Ins
titute
![Page 3: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/3.jpg)
Aakas
h Ins
titute
![Page 4: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/4.jpg)
Aakas
h Ins
titute
![Page 5: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/5.jpg)
EXERCISE 29.2 PAGE NO: 29.18 Evaluate the following limits:
Aak
ash I
nstitu
te
![Page 6: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/6.jpg)
Aakas
h Ins
titute
![Page 7: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/7.jpg)
EXERCISE 29.3 PAGE NO: 29.23 Evaluate the following limits:
Aakas
h Ins
titute
![Page 8: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/8.jpg)
Aakas
h Ins
titute
![Page 9: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/9.jpg)
∴ The value of the given limit is ½.
Aakas
h Ins
titute
![Page 10: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/10.jpg)
By substituting the value of x, we get Aak
ash I
nstitu
te
![Page 11: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/11.jpg)
Aakas
h Ins
titute
![Page 12: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/12.jpg)
EXERCISE 29.4 PAGE NO: 29.28 Evaluate the following limits:
Aakas
h Ins
titute
![Page 13: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/13.jpg)
∴ The value of the given limit is ½.
We need to find the limit of the given equation when x => 0
Now let us substitute the value of x as 0, we get an indeterminate form of 0/0.
Let us rationalizing the given equation, we get
Aakas
h Ins
titute
![Page 14: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/14.jpg)
Aakas
h Ins
titute
![Page 15: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/15.jpg)
Aak
ash I
nstitu
te
![Page 16: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/16.jpg)
∴ The value of the given limit is ½.
EXERCISE 29.5 PAGE NO: 29.33 Evaluate the following limits:
Aakas
h Ins
titute
![Page 17: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/17.jpg)
Aakas
h Ins
titute
![Page 18: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/18.jpg)
Aakas
h Ins
titute
![Page 19: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/19.jpg)
Aakas
h Ins
titute
![Page 20: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/20.jpg)
EXERCISE 29.6 PAGE NO: 29.38 Evaluate the following limits:
Aakas
h Ins
titute
![Page 21: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/21.jpg)
= 3 / 2
Aakas
h Ins
titute
![Page 22: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/22.jpg)
Aakas
h Ins
titute
![Page 23: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/23.jpg)
EXERCISE 29.7 PAGE NO: 29.49 Evaluate the following limits: Aak
ash I
nstitu
te
![Page 24: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/24.jpg)
So, Aak
ash I
nstitu
te
![Page 25: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/25.jpg)
Aakas
h Ins
titute
![Page 26: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/26.jpg)
Aakas
h Ins
titute
![Page 27: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/27.jpg)
EXERCISE 29.8 PAGE NO: 29.62 Evaluate the following limits:
Aakas
h Ins
titute
![Page 28: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/28.jpg)
Aakas
h Ins
titute
![Page 29: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/29.jpg)
Aakas
h Ins
titute
![Page 30: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/30.jpg)
Aakas
h Ins
titute
![Page 31: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/31.jpg)
EXERCISE 29.9 PAGE NO: 29.65 Evaluate the following limits:
Aakas
h Ins
titute
![Page 32: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/32.jpg)
Aakas
h Ins
titute
![Page 33: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/33.jpg)
Aakas
h Ins
titute
![Page 34: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/34.jpg)
Aakas
h Ins
titute
![Page 35: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/35.jpg)
Aakas
h Ins
titute
![Page 36: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/36.jpg)
EXERCISE 29.10 PAGE NO: 29.71 Evaluate the following limits:
Aakas
h Ins
titute
![Page 37: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/37.jpg)
Aakas
h Ins
titute
![Page 38: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/38.jpg)
Aakas
h Ins
titute
![Page 39: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/39.jpg)
Aakas
h Ins
titute
![Page 40: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/40.jpg)
EXERCISE 29.11 PAGE NO: 29.71 Evaluate the following limits:
Aak
ash I
nstitu
te
![Page 41: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/41.jpg)
Aakas
h Ins
titute
![Page 42: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/42.jpg)
So here,
f (x) = cos x + sin x – 1
g (x) = x
Then,
Aakas
h Ins
titute
![Page 43: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/43.jpg)
Aakas
h Ins
titute
![Page 44: RD Sharma Solutions for Class 11 Maths Chapter 29 Limits](https://reader033.vdocuments.us/reader033/viewer/2022051102/6276d1a15a53912f95575085/html5/thumbnails/44.jpg)
Aakas
h Ins
titute