NCERT Solutions for Class 12 Maths Exercise 5.3 Chapter 5 Continuity and Differentiability – FREE PDF Download
Free PDF download of NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3 (Ex 5.3) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.3 Questions with Solutions to help you to revise complete Syllabus and Score More marks.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.3 (Ex 5.3)
Find in the following Exercise 1 to 15.
1.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image002.png)
2. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image008.png)
3. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image014.png)
dydx(2by+siny)=−adydx(2by+siny)=−a
4. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image020.png)
[By Product Rule]
5. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image027.png)
6. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image033.png)
ddxx3+ddxx2y+ddxxy2+ddxy3=ddx81ddxx3+ddxx2y+ddxxy2+ddxy3=ddx81
dydx=−(3x2+2xy+y2)x2+2xy+3y2dydx=−(3×2+2xy+y2)x2+2xy+3y2
7. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image039.png)
8. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image046.png)
⟹ddx(sin2x)+ddx(cos2y)=ddx(1)⟹ddx(sin2x)+ddx(cos2y)=ddx(1)
9. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image054.png)
To simplify the given Inverse Trigonometric function, putting
=
10. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image060.png)
To simplify the given Inverse Trigonometric function, putting
11. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image065.png)
Putting
= =
=
12. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image071.png)
Putting
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image055.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image072.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image073.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image074.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image075.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image070.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image076.png)
13. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image077.png)
Putting
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image055.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image078.png)
= cos−1(sin2θ)cos−1(sin2θ)
=
=
14. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image081.png)
Putting
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image082.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image083.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image084.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image085.png)
=
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image086.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image070.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image087.png)
15. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image088.png)
Putting
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex5.3/image089.png)
y=sec−1(12cos2θ−1)y=sec−1(12cos2θ−1)
=
=
=