Recent questions tagged bookproblem

Differentiate w.r.t. $x$ the function in $ x^{\large x^2-3} + ( x - 3 )^{\large x^2} $, for $x > 3$

asked Nov 21, 2012 by thanvigandhi_1

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 $

asked Nov 21, 2012 by thanvigandhi_1

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} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ \cos \: (a \cos x + b \sin x) $ , for some constant $a$ and $b$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $( \log x )^{\large\log x}, x > 1 $

asked Nov 21, 2012 by thanvigandhi_1

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 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ sin^{-1}(x \: \sqrt x ), 0 \leq x \leq 1 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ sin^3x + cos^6x $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ (3x^2 - 9x + 5)^9 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

asked Nov 21, 2012 by thanvigandhi_1

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$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Mean Value Theorem, if $ f (x) = x^2 - 4x - 3 $ in the interval $ [a,b]$, where $ a = 1 $ and $b = 4 $.

asked Nov 21, 2012 by thanvigandhi_1

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)$.

asked Nov 21, 2012 by thanvigandhi_1

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] $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Verify Rolle's theorem for the function $ f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = ( tan^{-1}x )^2$, show that $ (x^2 + 1 )^2 \: y_2 + 2x (x^2 +1 ) \: y_1 = 2 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Consider the binary operation $ \wedge$ on the set $\{1, 2, 3, 4, 5\}$ defined by $a \wedge b = min \{a, b\}$. Write the multiplication table of the operation $ \wedge$ .

asked Nov 20, 2012 by vaishali.a

1 answer

For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative. $\begin{array}{1 1}(i) \;\;\; On\, Z,\, define \,ab\, = a-b & \;\\(ii) \;\;\; On\, Q,\, define \,ab\, = ab+1 & \;\\(iii) \;\;\; On\, Q,\, define \,ab\, = \frac {ab} {2} & \;\\(iv) \;\;\; On\, Z^+, \, define\, ab= 2^{ab} & \;\\(v) \;\;\; On\, Z^+,\, define \,ab\, = a^b & \;\\(vi) \;\;\; On R - \{ -1\},\, define\, ab= \frac {a} {b+1} & \;\end{array}$

asked Nov 20, 2012 by vaishali.a

5 answers

If $ e^y ( x + 1 ) = 1$, show that $ \large\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 500e^{\large 7x} + 600e^{\large -7x}$, show that $ \large\frac{d^2y}{dx^2}\normalsize = 49y$

asked Nov 20, 2012 by thanvigandhi_1

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 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 3 \cos \: (\log x ) + 4 \sin ( \log x )$, show that $x^2y_2 + xy_1 + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y =\cos^{-1}x $ , find $ \large\frac{d^2y}{dx^2}$ in terms of $ y $ alone.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 5 \cos x - 3 \sin x $ , prove that $ \large\frac{d^2y}{dx^2}\normalsize + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \sin (\log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log ( \log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \tan^{-1} x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of $ e^{6x} \cos 3x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the function $(e^{\large x} \sin 5x)$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^3 \log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x \; \cos x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^{\large 20} $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^2 + 3x + 2 $

asked Nov 20, 2012 by thanvigandhi_1

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} $

asked Nov 20, 2012 by thanvigandhi_1

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 $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

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 $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

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}$

asked Nov 20, 2012 by thanvigandhi_1

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 $\large\frac{ dy}{ dx}$.

asked Nov 20, 2012 by thanvigandhi_1

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 $\large\frac{dy}{dx}$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this - On$ \; Z^+,\,$ defined $\,$ by$\; ab= a-b $

asked Nov 19, 2012 by vaishali.a

1 answer

Let $f : R - \{ - \frac {4} {3} \} \to R $ be a function defined as $f(x)= \frac {4x} {3x+4} $ .The inverse of $f$ is the map $g$: Range $f \to R - \{ - \frac {4} {3} \} $ given by

asked Nov 19, 2012 by vaishali.a

1 answer

If $f: R\to R$ be given by $f(x)=(3-x^3)^\frac {1}{3} $, then $fof(x)$ is

asked Nov 19, 2012 by vaishali.a

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 $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

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 $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

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 $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

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 $\frac{\large dy}{\large dx}$

asked Nov 19, 2012 by thanvigandhi_1

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 $\frac{\large dy}{\large dx}$

asked Nov 17, 2012 by thanvigandhi_1

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.

asked Nov 17, 2012 by thanvigandhi_1

1 answer

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