Recent questions in Continuity and Differentiability

The value of c in Rolle's theorem for the function $f(x)=x^3-3x$ in the interval $[0,\sqrt 3]$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

If $x=t^2$,$y=t^3,then\;\large \frac{d^2y}{dx^2}$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

The derivative of $\cos^{-1}(2x^2-1)$ w.r.t $\cos^{-1}x$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=\sqrt{sin x+y}$, then $\Large \frac{dy}{dx}$ is equal to

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=log\bigg(\large \frac{1-x^2}{1+x^2}\normalsize \bigg),then\;\large \frac{dy}{dx}$ is equal to

asked Jan 2, 2013 by sreemathi.v

1 answer

Let $f(x)=|sin x|$,then

asked Jan 2, 2013 by sreemathi.v

1 answer

If $f(x)=\left \{\begin{array}{1 1}mx+1, & if\;x\leq\large\frac{\pi}{2}\\\sin x+n, & if\;x>\large\frac{\pi}{2}\end{array}\right.$,is continuous at $x=\large\frac{\pi}{2}$,then

asked Jan 2, 2013 by sreemathi.v

1 answer

If $f(x)=x^2\sin \frac{1}{x}$,when $x\neq0$,then the value of the function f at $x=0$,so that the function is continuous at $x=0$,is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=e^{|x|}$ is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=\cot x$ is discontinuous on the set

asked Jan 2, 2013 by sreemathi.v

1 answer

The set of points where the functions f given by $f(x)=|2x-1|\sin x$ is differentiable is

asked Jan 2, 2013 by sreemathi.v

1 answer

The function $f(x)=\Large \frac{4-x^2}{4x-x^3}$ is

asked Jan 2, 2013 by sreemathi.v

1 answer

If f(x)=2x and $g(x)=\Large {\frac{x^2}{2}}\normalsize+1$,then which of the following can be a discontinuous function

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx},\normalsize if\;y=\large x^{tan x}+\sqrt{\large\frac{x^2+1}{2}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x=\sin t$ and $y=\sin pt$, prove that $(1-x^2)\large \frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}+\normalsize p^2y=0$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x^my^n=(x+y)^{m+n}$,Prove that $(i)\;\large\frac{dy}{dx}=\frac{y}{x}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the values of p and q so that $f(x)=\left \{\begin{array}{1 1}x^2+3x+p, & if \;x\leq\;1\\qx+2, & if\;x>\;1\end{array}\right.$is differentiable at $x=1.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using mean value theorem,prove that there is a point on the curve $y=2x^2-5x+3$ between the points $A(1,0)$ and $B(2,1)$where tangent is parallel to chord $AB$. Also find the point.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find a point on the curve $y=(x-3)^2$,where the tangent is parallel to the chord joining the point (3,0) and (4,1).

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sqrt {25-x^2}\;in\;[1,5].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sin x-\sin 2x\;in\;[0,\pi].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=x^3-2x^2-x+3\;in\;[0,1].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\large\frac{1}{4x-1}$ in $[1,4].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using Rolle's theorem,find the point on the curve $y=x(x-4),x\in[0,4]$,where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the points on the curve $y=(\cos x-1)$ in [0,2$\pi$],where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Discuss the applicability of Rolle's theorem on the function given by $f(x)=\left \{\begin{array}{1 1}x^2+1, & if\;0\leq x\leq1\\3\;x, & if\;1<x<2\end{array}\right.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sqrt {4-x^2}\;in\;[-2,2]$

asked Jan 2, 2013 by sreemathi.v

1 answer

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

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