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Recent questions tagged ch5

Verify the Rolle's theorem for the function $f(x)=x(x+3)e^{\large-x/2}\;in\;[-3,0]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $log(x^2+2)-log 3\;in\;[-1,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sin^4x+\cos^4x\;in\;\begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=x(x-1)^2\;in\;[0,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

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

asked Jan 2, 2013 by sreemathi.v

1 answer

If $\sqrt {1-x^2}+\sqrt {1-y^2}=a(x-y),$prove that $\large \frac{dy}{dx}=\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}$.

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x\sin(a+y)+\sin a\cos(a+y)=0,prove\;that\;\large {\frac{dy}{dx}=\frac{\sin^2(a+y)}{\sin a}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y=(\cos x)^{\Large(\cos x)^{(\Large \cos x)..........\infty.}},$show that $\large {\frac{dy}{dx}=\frac{y^2\tan x}{ylog\cos x-1}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y^{\large x}=e^{\large y-x},prove\;that\;\large {\frac{dy}{dx}=\frac{(1+logy)^2}{log y}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x=e^{\Large \frac{x}{y}},prove\; that \; \large {\frac{dy}{dx}=\frac{x-y}{xlog x}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $ax^2+2hxy+by^2+2gx+2fy+c=0$,then show that $\large \frac{dy}{dx}.\frac{dx}{dy}\normalsize =1$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $(x^2+y^2)^2=xy$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\tan^{-1}(x^2+y^2)=a $

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\sec(x+y)=xy$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\;\sin(xy)+\large\frac{x}{y}$$=x^2-y$

asked Jan 1, 2013 by sreemathi.v

1 answer

Differentiate $ tan^{-1}\bigg (\Large \frac{\sqrt {1+x^2}-1}{x}\bigg)\;\normalsize w.r.t\;\tan^{-1}x\;when\;x\neq 0$

asked Jan 1, 2013 by sreemathi.v

1 answer

Differentiate $\large \frac{x}{\sin x}\;\normalsize w.r.t\;\sin x.$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=3\sin t-\sin 3t,y=3\cos t-\cos 3t,find \;\large \frac{dy}{dx}\;\normalsize at \;t=\large \frac{\pi}{3}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=a\sin 2t(1+\cos 2t)\;and\;y=b\cos 2t(1-\cos 2t),show\;that\bigg(\large \frac{dy}{dx}\bigg)_{at\;t=\frac{\pi}{4}}=\frac{-b}{a}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=e^{\large\cos 2t}\; and\;y=e^{\large\sin 2t},prove\;that\;\large \frac{dy}{dx}=\frac{-ylog x}{xlog y}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=\large\frac{1+log t}{t^2},$$y=\large\frac{3+2log t}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $\sin x=\large\frac{2t}{1+t^2},$$\tan y=\large\frac{2t}{1-t^2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=3\cos \theta-2\cos^3\theta,y=3\sin \theta-2\sin^3\theta$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=e^\theta\bigg(\theta+\frac{1}{\theta}\bigg),y=e^{-\theta}\bigg(\theta-\frac{1}{\theta}\bigg)$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=t+\large\frac{1}{t},$$y=t-\large\frac{1}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\Large {\bigg(\frac{\sqrt {1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\bigg)},\normalsize -1 < x < 1,x\neq 0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sec^{-1}\bigg(\Large \frac{1}{4x^3-3x}\bigg),\normalsize 0 < x <\Large \frac{1}{\sqrt 2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\bigg(\large {\frac {a \cos x - b \sin x}{b \cos x + a \sin x}}\bigg)$, where $\frac{-\pi}{2} < x < \frac{\pi}{2}$ and $\frac{a}{b} \tan x > -1$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x:$\tan^{-1}(\sec x+\tan x),\large \frac{-\pi}{2}<$$x<\large\frac{\pi}{2}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x:$\tan^{-1}\bigg(\sqrt{\large\frac{1-\cos x}{1+\cos x}}\bigg),$$\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sin^{-1} \big[\large\frac{1}{\sqrt 2}$$\sin x+\large\frac{1}{\sqrt 2}$$\cos x\big],\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$: $(x+1)^2(x+2)^3(x+3)^4$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\sin^mx.\cos ^nx$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $(\sin x)^{\large\cos x}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\sin^{-1}\bigg|\large\frac{1}{\sqrt {x+1}}\bigg|$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sin (x^2)+\sin^2x+\sin^2(x^2)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\cos\bigg(\tan\sqrt {x+1}\bigg)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\sin^n(ax^2+bx+c)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sin\sqrt x+\cos^2\sqrt x$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $log\begin{bmatrix}log\bigg(log x^5\bigg)\end{bmatrix}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $log\bigg(x+\sqrt{ x^2+a}\bigg)$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ :$\large \frac{8^x}{x^8}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$: $2^{\large \cos^2x}$

asked Dec 31, 2012 by sreemathi.v

1 answer

A function $f\;:\;R\rightarrow R$ satisfies the equation $f(x+y)=f(x)f(y)$ for all $x,y\in R,f(x)\neq 0.$ Suppose that the function is differentiable at $x=0$ and $f'(0)=2$.Prove that $f'(x)=2f(x).$

asked Dec 31, 2012 by sreemathi.v

1 answer

Show that $f(x)=|x-5|$ is continuous but not differentiable at $x=5$

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}1+x, & if\;x\leq 2\\5-x, & if\;x>2\end{array}\right.$at $x=2$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the differentiability of $f$,where $f$ is defined by $f(x)=\left \{\begin{array}{1 1}x^2\sin\large\frac{1}{x}, & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at $x=0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}x[x], & if\;0\leq x<2\\(x-1)x, & if\;2\leq x<3\end{array}\right.$at $x=2$

asked Dec 31, 2012 by sreemathi.v

1 answer

Show that the function $f(x)=\mid \sin x+\cos x\mid$ is continuous at $x=\pi$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find all points of discontinuity of the function $f(t)=\large\frac{1}{t^2+t-2},$where $\;t=\large\frac{1}{x-1}.$

asked Dec 31, 2012 by sreemathi.v

1 answer

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