Quantcast
Viewing all articles
Browse latest Browse all 9412

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7

Get Free NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Continuity and Differentiability Exercise 5.7 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 5 Class 12 Continuity and Differentiability Ex 5.7 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

The topics and sub-topics included in the Continuity and Differentiability chapter are the following:

  • Continuity and Differentiability
  • Introduction
  • Algebra of continuous functions
  • Differentiability
  • Derivatives of composite functions
  • Derivatives of implicit functions
  • Derivatives of inverse trigonometric functions
  • Exponential and Logarithmic Functions
  • Logarithmic Differentiation
  • Derivatives of Functions in Parametric Forms
  • Second Order Derivative
  • Mean Value Theorem
  • Summary

There are total eight exercises and one misc exercise(144 Questions fully solved) in the class 12th maths chapter 5 Continuity and Differentiability.

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7

Find the second order derivatives of the functions given in Questions 1 to 10.

Ex 5.7 Class 12 Maths Question 1.
x² + 3x + 2 = y(say)
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =2x+3\quad and\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =2

Ex 5.7 Class 12 Maths Question 2.
x20 = y(say)
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } ={ 20 }x^{ 19 }\quad =>\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =20\times { 19x }^{ 18 }={ 380 }x^{ 18 }\qquad

Ex 5.7 Class 12 Maths Question 3.
x.cos x = y(say)
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =x(-sinx)+cosx.1,=-xsinx+cosx

Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =-xcosx-sinx-sinx=-xcosx-2sinx

Ex 5.7 Class 12 Maths Question 4.
log x = y (say)
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =\frac { 1 }{ x } =>\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =-\frac { 1 }{ { x }^{ 2 } }

Ex 5.7 Class 12 Maths Question 5.
x3 log x = y (say)
Solution:
x3 log x = y
Image may be NSFW.
Clik here to view.
=>\frac { dy }{ dx } ={ x }^{ 3 }.\frac { 1 }{ x } +logx\times { 3x }^{ 2 }={ x }^{ 2 }+{ 3x }^{ 2 }logx

Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =2x+{ 3x }^{ 2 }.\frac { 1 }{ x } +logx.6x=x(5+6logx)

Ex 5.7 Class 12 Maths Question 6.
ex sin5x = y
Solution:
ex sin5x = y
Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 6

Ex 5.7 Class 12 Maths Question 7.
e6x cos3x = y
Solution:
e6x cos3x = y
Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 7

Ex 5.7 Class 12 Maths Question 8.
tan-1 x = y
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =\frac { 1 }{ 1+{ x }^{ 2 } } =>\frac { { d }^{ 2y } }{ { dx }^{ 2 } } =\frac { -2x }{ { ({ 1+x }^{ 2 }) }^{ 2 } }

Ex 5.7 Class 12 Maths Question 9.
log(logx) = y
Solution:
log(logx) = y
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =\frac { 1 }{ logx } .\frac { 1 }{ x }

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 9

Ex 5.7 Class 12 Maths Question 10.
sin(log x) = y
Solution:
sin(log x) = y
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =\frac { cos(logx) }{ x }

Image may be NSFW.
Clik here to view.
and\quad \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =\frac { x.\left[ -sin(logx) \right] .\frac { 1 }{ x } -cos(logx).1 }{ { x }^{ 2 } }

Image may be NSFW.
Clik here to view.
=\frac { \left[ sin(logx)+cos(logx) \right] }{ { x }^{ 2 } }

Ex 5.7 Class 12 Maths Question 11.
If y = 5 cosx – 3 sin x, prove that Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0

Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =-5sinx-3cosx

Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =-5cosx+3sinx=-y

Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0

Hence proved

Ex 5.7 Class 12 Maths Question 12.
If y = cos-1 x, Find Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }
in terms of y alone.
Solution:
Image may be NSFW.
Clik here to view.
\frac { dy }{ dx } =-{ \left( { 1-x }^{ 2 } \right) }^{ -\frac { 1 }{ 2 } }

Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =\frac { -cosy }{ { \left( { sin }^{ 2 }y \right) }^{ \frac { 3 }{ 2 } } } =-coty\quad { cosec }^{ 2 }y

Ex 5.7 Class 12 Maths Question 13.
If y = 3 cos (log x) + 4 sin (log x), show that
Image may be NSFW.
Clik here to view.
{ x }^{ 2 }{ y }_{ 2 }+{ xy }_{ 1 }+y=0

Solution:
Given that
y = 3 cos (log x) + 4 sin (log x)
Image may be NSFW.
Clik here to view.
tiwari academy class 12 maths Chapter 5 Continuity and Differentiability 13

Ex 5.7 Class 12 Maths Question 14.
Image may be NSFW.
Clik here to view.
If\quad y=A{ e }^{ mx }+B{ e }^{ nx },\quad show\quad that\quad \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -(m+n)\frac { dy }{ dx } +mny=0

Solution:
Given that
Image may be NSFW.
Clik here to view.
\quad y=A{ e }^{ mx }+B{ e }^{ nx },\quad

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 14

Ex 5.7 Class 12 Maths Question 15.
If y = 500e7x + 600e-7x, show that Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =49y
.
Solution:
we have
y = 500e7x + 600e-7x
Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 15

Ex 5.7 Class 12 Maths Question 16.
If ey(x+1) = 1,show that Image may be NSFW.
Clik here to view.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }

Solution:
Image may be NSFW.
Clik here to view.
{ e }^{ y }(x+1)=1=>{ e }^{ y }=\frac { 1 }{ x+1 }

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 16

Ex 5.7 Class 12 Maths Question 17.
If y=(tan-1 x)² show that (x²+1)²y2+2x(x²+1)y1=2
Solution:
we have
y=(tan-1 x)²
Image may be NSFW.
Clik here to view.
tiwari academy class 12 maths Chapter 5 Continuity and Differentiability 17

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Hindi Medium Ex 5.7

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity updated for 2018-19

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity for CBSE and UP Board students

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity in English medium

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity question 11, 12, 13, 14, 15, 16, 17

Image may be NSFW.
Clik here to view.
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity in Hindi medium

Image may be NSFW.
Clik here to view.
Class 12 Maths exercise 5.7 Solutions

Image may be NSFW.
Clik here to view.
Class 12 Maths exercise 5.7 Solutions in Hindi

Image may be NSFW.
Clik here to view.
Class 12 Maths exercise 5.7 Solutions of all questions

Image may be NSFW.
Clik here to view.
Class 12 Maths exercise 5.7 Sols in Hindi for CBSE and UP Board session 2018-19

Image may be NSFW.
Clik here to view.
12 Maths Chapter 5 Exercise 5.7 Continuity in Hindi medium

NCERT Class 12 Maths Solutions

The post NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7 appeared first on Learn CBSE.


Viewing all articles
Browse latest Browse all 9412

Trending Articles



<script src="https://jsc.adskeeper.com/r/s/rssing.com.1596347.js" async> </script>