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Recent questions tagged limits-of-trigonometric-functions

Evaluate $\lim \limits _{x \to \pi/6} \large\frac{(\sqrt 3 \sin x - \cos x)}{(x-\pi/6)}$

asked Apr 22, 2014 by meena.p

1 answer

If the function $f(x)=\left\{\begin{array}{1 1}(\cos x)^{1/x}&x\neq 0\\k&x=0\end{array}\right.$ is continuous at $x=0$ then value of $K$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

let $\alpha$ and $\beta$ be the distinct roots of $ax^2+bx+c=0$ then $\lim\limits_{x\to \alpha}\large\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$ is equal to

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\large\frac{\sin(e^x-1)}{\log x}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\cos(\large\frac{x}{2})$$\cos(\large\frac{x}{4})$$\cos(\large\frac{x}{8})$$........\cos(\large\frac{x}{2^n})$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

The value of $\lim\limits_{x\to 0}\big((\sin x)^{1/x}+(1+x)^{\large\sin x}\big)$ where $x > 0$ is

asked Jan 3, 2014 by sreemathi.v

1 answer

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

asked Jan 2, 2014 by sreemathi.v

1 answer

If $f(x)$ is the integral function of the function $\large\frac{2\sin x-\sin 2x}{x^3}\qquad$$ x\neq 0$ then $\lim\limits_{x\to 0} f'(x)$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\big[\sec\big(\large\frac{\pi x}{2}\big)$$\log x\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

The value of $\lim\limits_{n\to \infty}x\bigg[\tan^{-1}\large\frac{x+1}{x+2}$$-\cot^{-1}\large\frac{x+2}{x}\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\sin x}{x}$

asked Dec 31, 2013 by sreemathi.v

1 answer

Find $\lim\limits_{x\to 0}\{\tan(\large\frac{\pi}{4}$$+x)\}^{1/x}$

asked Dec 31, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to {-1}}\large\frac{\sqrt{\pi}-\sqrt{\cos^{-1}x}}{\sqrt{x+1}}$ is given by

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\cos x-\sin x}{(\Large\frac{\pi}{4}-\normalsize x)(\large\cos x+\sin x)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \large\frac{\pi}{4}}\big(\large\frac{1-\tan x}{1\sqrt 2\sin x}\big)$=

asked Dec 30, 2013 by sreemathi.v

1 answer

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

asked Dec 30, 2013 by sreemathi.v

1 answer

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

asked Dec 30, 2013 by sreemathi.v

1 answer

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

asked Dec 24, 2013 by sreemathi.v

1 answer

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

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

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

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

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

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

asked Dec 24, 2013 by sreemathi.v

1 answer

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

asked Dec 24, 2013 by sreemathi.v

1 answer

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

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

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

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

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

asked Dec 20, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}(1-x)\tan\large\frac{\pi x}{2}$=__________

asked Dec 20, 2013 by sreemathi.v

1 answer

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