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Recent questions tagged class12

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\cot x}{\cot 2x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\log _{e}x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\frac{1}{x^{2}}-\large 2\tan^{-1}(\frac{1}{x})}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty}\large\frac{\sin\frac{2}{x}}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 2}\large\frac{x^{n}-2^{n}}{x-2}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0}\large\frac{\sin ^{-1} x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\tan x-x}{x- \sin x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists.$\;\lim\limits_{x\to 2} \large\frac{\sin \pi x}{2 - x}$

asked May 6, 2013 by poojasapani_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and also the distance from origin(b) $x+y+z=1$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $y=12x^{2}-2x^{3}-x^{4}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(\theta)=\sin 2\theta $ in $ (0 , \pi )$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{4}-6x^{2}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=2x^{3}+5x^{2}-4x$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{2}-x$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions:$f(x)=(x-1)^{1/3}$

asked May 6, 2013 by poojasapani_1

0 answers

Resistance to motion,$F$, of a moving vehicle is given by,$F=\large\frac{5}{x}$$+100x.$ Determine the minimum value of resistance.

asked May 6, 2013 by poojasapani_1

1 answer

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius $r$.

asked May 6, 2013 by poojasapani_1

1 answer

Show that of all the rectangles with a given perimeter the one with the greatest area is a square.

asked May 5, 2013 by poojasapani_1

1 answer

Show that of all the rectangles with a given area the one with smallest perimeter is a square.

asked May 5, 2013 by poojasapani_1

1 answer

Find two positive numbers whose product is $100$ and whose sum is minimum.

asked May 5, 2013 by poojasapani_1

1 answer

Find two numbers whose sum is $100 $ and whose product is a maximum.

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $t+ \cos t$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $\sin^{2} \theta , [0 ,\pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $(x^{2}-1)^{3}$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $x^{4}-6x^{2}$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $2x^{3}+5x^{2}-4x $

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $x^{3}-x$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x-2\cos x , [-\pi ,\pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sin x +\cos x ,[0 ,\large\frac {\pi}{3}]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\large\frac{x}{x+1},$$ [1 , 2 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sqrt{9-x^{2}} ,[-1 , 2]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{3}-12x+1 ,[-3 , 5]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=1-2x-x^{2}, [-4 , 1 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{2}-2x+2 , [0 , 3 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(\theta)=\theta+\sin\theta$ in $[0 , 2\pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the critical numbers and stationary points of each of the following functions. $\;f(\theta)=\sin^{2} 2\theta \;$in$\;[0 , \pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=\large\frac{x+1}{x^{2}+x+1}$

asked May 5, 2013 by poojasapani_1

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=x^{4/5}(x-4)^{2}$

asked May 5, 2013 by poojasapani_1

0 answers

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=x^{3}-3x+1$

asked May 5, 2013 by poojasapani_1

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=2x-3x^{2}$

asked May 5, 2013 by poojasapani_1

1 answer

If $f:R\rightarrow S$ defined by $\:f(x)=\sin x-\sqrt3\; \cos x+1\;$ is onto function then $S$ = ?

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

Prove the following inequalities: $\log(1+ x)< x $ for all $x>0$

asked May 4, 2013 by poojasapani_1

1 answer

Prove the following inequalities: $\tan ^{-1}x < x$ for all $x>0$

asked May 4, 2013 by poojasapani_1

1 answer

Prove the following inequalities: $\sin x> x-\large\frac{x^{3}}{6}, $$x>0$

asked May 4, 2013 by poojasapani_1

1 answer

If $f$ is a real values function satisfying $f(x+y)=f(x)\;f(y)$ and $f(1)=a$ where $x,y\in R$, then $f(x)$ =

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

Prove the following inequalities: $\cos x> 1-\large\frac{x^{2}}{2}, $$x>0$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=\sin^{4}x+\cos^{4}x $ in $ [0 , \large\frac{\pi}{2}]$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x+\cos x $ in $[0 , \pi ]$

asked May 4, 2013 by poojasapani_1

1 answer

The value of $\alpha$ for which the function $f(x)=1+\alpha x,\:\:\alpha\neq 0$ is the inverse of itself is:

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x-2\sin x,[0 , 2\pi ]$

asked May 4, 2013 by poojasapani_1

1 answer

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