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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Find \(\large \frac{dy}{dx} \), if \( y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 \)
cbse
class12
bookproblem
ch5
misc
q13
p191
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Find \( \large\frac{dy}{dx} \), if \( y = 12 ( 1 - \cos t ) , x = 10 ( t - \sin t ) , -\large\frac{\pi}{2}\normalsize < t <\large \frac{\pi}{2} \)
cbse
class12
bookproblem
ch5
misc
q12
p191
easy
sec-b
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( x^{\large x^2-3} + ( x - 3 )^{\large x^2} \), for \(x > 3\)
cbse
class12
bookproblem
ch5
misc
q11
p191
sec-c
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( x^{\large x} + x^{\large a} + a^{\large x} + a^{\large a} \), for some fixed \( a > 0 \) and \( x > 0 \)
cbse
class12
bookproblem
ch5
misc
q10
p191
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( (\sin x - \cos x )^{\large(\sin x - \cos x )} , \large\frac {\pi}{4}\normalsize < x < \large\frac{3\pi}{4} \)
cbse
class12
bookproblem
ch5
misc
q9
p191
sec-b
easy
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( \cos \: (a \cos x + b \sin x) \) , for some constant \(a\) and \(b\)
cbse
class12
bookproblem
ch5
misc
q8
p191
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \(( \log x )^{\large\log x}, x > 1 \)
cbse
class12
bookproblem
ch5
misc
q7
p191
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \(\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 \)
cbse
class12
bookproblem
ch5
misc
q5
p191
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( sin^{-1}(x \: \sqrt x ), 0 \leq x \leq 1 \)
cbse
class12
bookproblem
ch5
misc
q4
p191
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $
cbse
class12
bookproblem
ch5
misc
q3
p191
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( sin^3x + cos^6x \)
cbse
class12
bookproblem
ch5
misc
q2
p191
sec-c
medium
math
asked
Nov 21, 2012
1
answer
Differentiate w.r.t. \(x\) the function in \( (3x^2 - 9x + 5)^9 \)
cbse
class12
bookproblem
ch5
misc
q1
p191
sec-b
easy
math
asked
Nov 21, 2012
1
answer
Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$
cbse
class12
bookproblem
ch5
sec8
q6
q6-1
p186
sec-a
easy
math
asked
Nov 21, 2012
1
answer
Verify Mean Value Theorem, if \( f (x) = x^3 - 5x^2 - 3x \) in the interval \( [a,b]\), where \( a = 1\) and \( b = 3\). Find all \( c \in (1,3) \) for which \( f'(c) = 0\).
cbse
class12
bookproblem
ch5
sec8
q5
p186
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Verify Mean Value Theorem, if \( f (x) = x^2 - 4x - 3 \) in the interval \( [a,b]\), where \( a = 1 \) and \(b = 4 \).
cbse
class12
bookproblem
ch5
sec8
q4
p186
sec-b
easy
math
asked
Nov 21, 2012
1
answer
If \( f : [ -5,5] \rightarrow R \) is a differentiable function and if \( f' (x) \) does not vanish anywhere, then prove that \( f (-5) \: \neq \: f (5)\).
cbse
class12
bookproblem
ch5
sec8
q3
p186
sec-b
medium
math
asked
Nov 21, 2012
1
answer
Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? $(i)\;f (x) = [x] \;for\; x \: \in [5,9] $
cbse
class12
bookproblem
ch5
sec8
q2
p186
math
sec-a
asked
Nov 20, 2012
1
answer
Verify Rolle's theorem for the function \( f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. \)
cbse
class12
bookproblem
ch5
sec8
q1
p186
sec-a
easy
math
asked
Nov 20, 2012
1
answer
If \( y = ( tan^{-1}x )^2\), show that \( (x^2 + 1 )^2 \: y_2 + 2x (x^2 +1 ) \: y_1 = 2 \)
cbse
class12
bookproblem
ch5
sec7
q17
p184
sec-a
medium
math
asked
Nov 20, 2012
1
answer
If \( e^y ( x + 1 ) = 1\), show that \( \large\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2\)
cbse
class12
bookproblem
ch5
sec7
q16
p184
sec-b
easy
math
asked
Nov 20, 2012
1
answer
If \( y = 500e^{\large 7x} + 600e^{\large -7x}\), show that \( \large\frac{d^2y}{dx^2}\normalsize = 49y\)
cbse
class12
bookproblem
ch5
sec7
q15
p184
sec-a
easy
math
asked
Nov 20, 2012
1
answer
If \( y = Ae^{mx} + Be^{nx}\), show that \( \large\frac{d^2y}{dx^2} -\normalsize ( m + n ) \large\frac{dy}{dx} +\normalsize mny = 0 \)
cbse
class12
bookproblem
ch5
sec7
q14
p184
sec-b
easy
math
asked
Nov 20, 2012
1
answer
If \( y = 3 \cos \: (\log x ) + 4 \sin ( \log x )\), show that \(x^2y_2 + xy_1 + y = 0\)
cbse
class12
bookproblem
ch5
sec7
q13
p184
sec-a
easy
math
asked
Nov 20, 2012
1
answer
If \( y =\cos^{-1}x \) , find \( \large\frac{d^2y}{dx^2}\) in terms of \( y \) alone.
cbse
class12
bookproblem
ch5
sec7
q12
p184
sec-b
medium
math
asked
Nov 20, 2012
1
answer
If \( y = 5 \cos x - 3 \sin x \) , prove that \( \large\frac{d^2y}{dx^2}\normalsize + y = 0\)
cbse
class12
bookproblem
ch5
sec7
q11
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ \sin (\log x) $
cbse
class12
bookproblem
ch5
sec7
q10
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $\log ( \log x) $
cbse
class12
bookproblem
ch5
sec7
q9
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ \tan^{-1} x $
cbse
class12
bookproblem
ch5
sec7
q8
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of $ e^{6x} \cos 3x$
cbse
class12
bookproblem
ch5
sec7
q7
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the function $(e^{\large x} \sin 5x)$
cbse
class12
bookproblem
ch5
sec7
q6
p183
sec-a
medium
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ x^3 \log x $
cbse
class12
bookproblem
ch5
sec7
q5
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $\log x $
cbse
class12
bookproblem
ch5
sec7
q4
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ x \; \cos x$
cbse
class12
bookproblem
ch5
sec7
q3
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ x^{\large 20} $
cbse
class12
bookproblem
ch5
sec7
q2
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
Find the second order derivatives of the functions given in $ x^2 + 3x + 2 $
cbse
class12
bookproblem
ch5
sec7
q1
p183
sec-a
easy
math
asked
Nov 20, 2012
1
answer
If $x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} $, show that $\frac {\large dy}{\large dx} = -\frac{\large y}{\large x} $
cbse
class12
bookproblem
ch5
sec6
q11
p181
medium
sec-c
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = a ( \cos \theta + \theta \sin \theta), y = a ( \sin \theta - \theta \cos \: \theta) $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.
cbse
class12
bookproblem
ch5
sec6
q10
p181
sec-a
easy
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $x = a \sec \theta, y = b \tan \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.
cbse
class12
bookproblem
ch5
sec6
q9
p181
easy
sec-a
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $x = a \big(\cos t +\ log \tan \large\frac{t}{2}\big) $ and $ y = a \sin t $ without eliminating the parameter, Find $ \frac{\large dy}{\large dx}$
cbse
class12
bookproblem
ch5
sec6
q8
p181
sec-b
medium
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = \large\frac{\sin^3t}{\sqrt {\cos 2t}}, $$y = \large\frac{\cos^3t}{\sqrt {\cos 2t}} $ without eliminating the parameter, Find $\large\frac{ dy}{ dx}$.
cbse
class12
bookproblem
ch5
sec6
q7
p181
difficult
sec-c
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $x = a ( \theta - \sin \theta ), y = a ( 1 +\cos \theta) $ without eliminating the parameter, Find $\large\frac{dy}{dx}$
cbse
class12
bookproblem
ch5
sec6
q6
p181
easy
sec-b
math
asked
Nov 20, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = \cos \theta -\ cos 2\theta, y = \sin \theta -\ sin 2\theta $ without eliminating the parameter, Find $\large\frac{dy}{dx}$
cbse
class12
bookproblem
ch5
sec6
q5
p181
easy
sec-b
math
asked
Nov 19, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $x = 4t, \: y = \large\frac{4}{t} $ without eliminating the parameter, Find $\large\frac{dy}{dx}$
cbse
class12
bookproblem
ch5
sec6
q4
p181
easy
sec-a
math
asked
Nov 19, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = \sin t, y = \cos 2t $ without eliminating the parameter, Find $\large\frac{dy}{dx}$
cbse
class12
bookproblem
ch5
sec6
q3
p181
easy
sec-b
math
asked
Nov 19, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = a \cos \theta, y = b \cos \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$
cbse
class12
bookproblem
ch5
sec6
q2
p181
easy
sec-a
math
asked
Nov 19, 2012
1
answer
If $x$ and $y$ are connected parametrically by the equations given in $ x = 2at^2, \: y = at^4 $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$
cbse
class12
bookproblem
ch5
sec6
q1
p181
easy
sec-a
math
asked
Nov 17, 2012
1
answer
If $u,\: v$ and $w$ are functions of $x$, then show that $\large\frac{d}{dx} $$( u.v.w) =\large \frac{du}{dx} $$v.w + u . \large\frac{dv}{dx} $$. w + u.v. \large\frac{dw}{dx} $ in two ways - first by repeated application of product rule, second by logarithmic differentiation.
cbse
class12
bookproblem
ch5
sec5
q18
p179
medium
sec-b
math
asked
Nov 17, 2012
1
answer
Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?
cbse
class12
bookproblem
ch5
sec5
q17
p178
easy
sec-c
math
asked
Nov 17, 2012
1
answer
Find the derivative of the function given by $f(x) =( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)$ and hence find $ f' (1).$
cbse
class12
bookproblem
ch5
sec5
q16
p178
easy
sec-b
math
asked
Nov 17, 2012
1
answer
Find $\large\frac{dy}{dx}$ of the function $xy = e^{\large(x-y)}$
cbse
class12
bookproblem
ch5
sec5
q15
p178
medium
sec-a
math
asked
Nov 17, 2012
1
answer
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