Recent questions tagged class11

$\lim\limits_{h\to 0}\large\frac{f(2h+2+h^2)-f(2)}{f(h-h^2+1)-f(1)}$ given that $f'(2)=6$ and $f'(1)=4$

asked Dec 30, 2013 by sreemathi.v

1 answer

Let $f:R\to R$ be such that $f(1)=3$ and $f'(1)=6$.Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$ equals

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{\theta \to \Large\frac{\pi}{2}}(\sec\theta-\tan\theta)$=

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to 0}\large\frac{\tan x-\sin x}{x^3}$=

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to \infty}[x-\sqrt{x^2+x}]$=

asked Dec 24, 2013 by sreemathi.v

1 answer

If $f(5)=15,f'(5)=3$ then $\lim\limits_{x\to 5}\large\frac{xf(5)-5f'(x)}{x-5}$ is

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to a}\large\frac{\log(x-a)}{\log(e^x-e^a)}$ is

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to\Large\frac{\pi}{6}}\large\frac{3\sin x-\sqrt 3\cos x}{6x-\pi}$ equals

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\cos(\sin x)-1}{x^2}$=

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to \infty}\big(\large\frac{x+a}{x+b}\big)^{x+b}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

If $f(x)=\left\{\begin{array}{1 1}\large\frac{\sin[x]}{[x]}&[x]\neq 0\\0&[x]=0\end{array}\right.$ then

asked Dec 24, 2013 by sreemathi.v

1 answer

$f(x)=\large\frac{\log(1+ax)-\log(1-bx)}{x}$ is not defined at $x=0$ .The value which should be assigned to f at $x=0$.So that it is continuous at $x=0$ is

asked Dec 24, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to 0}\large\frac{\sin px}{\tan 3x}$$=4$ then value of p is

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\large\frac{(2x-3)(3x-4)}{(4x-5)(5x-6)}$=

asked Dec 24, 2013 by sreemathi.v

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$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cot x-1}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{(1-\cos 2x)\sin 5x}{x^2\sin 3x}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\sin x-x}{x^3}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cos x-1}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\bigg[\large\frac{x^3+2x^2+x+1}{x^2+2x+3}\bigg]^{\Large\frac{1-\cos(x-1)}{(x-1)^2}}$

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 2}\large\frac{2^x+2^{3-x}-6}{\sqrt{2^{-x}-2^{1-x}}}$ is

asked Dec 24, 2013 by sreemathi.v

1 answer

Value of $\lim_{x\to 2^-}\{x+(x-[x]^2)\}$ is

asked Dec 24, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}=e^2\qquad(a,b\in N)$ then

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\large\frac{x^3+x^2-2}{\sin(x-1)}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\big(\large\frac{a^x+b^x+c^x}{3}\big)^{\Large\frac{1}{x}}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{(\cos x)^{1/2}-(\cos x)^{1/3}}{\sin^2x}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\big(\large\frac{x+1}{x+2}\big)^{2x+1}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{n\to\infty}\bigg[\large\frac{1}{1-n^4}+\frac{1}{1-n^4}+.........+\frac{n^3}{1-n^4}\bigg]$

asked Dec 23, 2013 by sreemathi.v

1 answer

If $f(x)=\mid x-25\mid$ and $g(x)=f(f(x))$,find $g'(x)$ for $x > 50$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate :$\lim\limits_{x\to 0}(\cos x)^{\large\frac{1}{x^2}}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate :$\lim\limits_{x\to \Large\frac{\pi}{4}}\large\frac{\sqrt 2-\cos x-\sin x}{(4x-\pi)^2}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate : $\lim\limits_{x\to\large\frac{\pi}{2}}\large\frac{\sin(\cos x)\cos x}{\sin x-cosec x}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate : $\lim\limits_{x\to 0}\large\frac{e^x-e^{x\cos x}}{x+\sin x}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate : $\lim\limits_{x\to 0}(1+\sin x)^{\Large\frac{1}{x^2}}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate : $\lim\limits_{h\to 0}\large\frac{(a+h)^2\sin(a+h)-a^2\sin a}{h}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Let $f : R\rightarrow [0,\infty]$ be such that $\lim\limits_{x\to 5}f(x)$ exists and $\lim\limits_{x\to 5}\large\frac{(f(x))^2-9}{\sqrt{|x-5|}}$ = 0. Then $\lim\limits_{x\to 5}f(x)$ equals

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 2}\big(\large\frac{\sqrt{1-\cos 2(x-2)}}{x-2}\big)$

asked Dec 23, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to 0}\large\frac{\log(3+x)-\log(3-x)}{x}$$=K$ the value of $K$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

If $f(x+y)=f(x).f(y) \forall x,y$ and $f(5)=2,f'(0)=3$ then $f'(5)$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

If $f(1)=1,f'(1)=2$ then $\lim\limits\large\frac{\sqrt{f(x)-1}}{\sqrt x-1}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\log x^n-[x]}{[x]}$ $n\in N$ ($x$ denotes greatest integer less than or equal to $x$)

asked Dec 23, 2013 by sreemathi.v

1 answer

Let $f(x)=4$ and $f'(x)=4$. Then $\lim\limits_{x\to 2}\large\frac{xf(2)-2f(x)}{x-2}$ is given by

asked Dec 20, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\sin(\pi\cos^2x)}{x^2}$ equals

asked Dec 20, 2013 by sreemathi.v

1 answer

For $x\in R\lim\limits_{x\to \infty}\big(\large\frac{x-3}{x+2}\big)^x$=

asked Dec 20, 2013 by sreemathi.v

1 answer

If $G(x)=-\sqrt{25-x^2}$ then $\lim\limits_{x \to 1}\large\frac{G(x)-G(1)}{x-1}$ has the value

asked Dec 20, 2013 by sreemathi.v

1 answer

If $f(x)=\sqrt{\large\frac{x-\sin x}{x+\cos^2x}}$ then $\lim\limits_{x\to \infty}f(x)$ is

asked Dec 20, 2013 by sreemathi.v

1 answer

Find the equation of parabola with vertex (2,-3) and directrix x-4y-48=0.

asked Dec 20, 2013 by pranav_anshul

1 answer

$\lim\limits_{x\to \infty}\big(\large\frac{x+6}{x+1}\big)^{x+4}$=

asked Dec 20, 2013 by sreemathi.v

1 answer

If $f(9)=9,f'(9)=4$ then $\lim\limits_{x\to 9}\large\frac{\sqrt{f(x)}-3}{\sqrt x-3}$ equals

asked Dec 20, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to -\infty}\bigg[\large\frac{x^4\sin(1/x)+x^2}{(1+|x|^3)}\bigg]$=

asked Dec 20, 2013 by sreemathi.v

1 answer

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