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Recent questions in Limit, Continuity and Differentiability

Questions >> JEEMAIN and NEET >> Mathematics >> Limit, Continuity and Differentiability

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

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{n\to \infty}\sum\limits_{r=1}^n\large\frac{\pi}{n}$$\sin\large\frac{\pi r}{n}$ is

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

The function $f(x)=\left\{\begin{array}{1 1}1&x\leq -1\\|x|&-1< x < 1\\0&x\geq 1\end{array}\right.$

asked Dec 24, 2013 by sreemathi.v

1 answer

If $f(x)=(x+1)^{\cot x}$ is continuous at $x=0$ then $f(0)$ is

asked Dec 24, 2013 by sreemathi.v

2 answers

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

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{n\to\infty}\large\frac{n^p\sin^2(n!)}{n+1}$$\qquad0 < p < 1$ is equal to

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

The function $f(x)=\sin^{-1}(\cos x)$ is

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

$\lim\limits_{x\to 1}(\log_33x)^{\log_x3}$ is

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

If function $f(x)$ is differentiable at $x=a$ then $\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(x)}{x-a}$ is

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

Let $f : R\rightarrow R$ be a positive increasing function with $\lim\limits_{x\to 0}\large\frac{f(3x)}{f(x)}$$=1$. Then $\lim\limits_{x\to \infty}\large\frac{f(2x)}{f(x)}$ = ?

asked Dec 23, 2013 by sreemathi.v

1 answer

Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f'(x)\geq 2$ for $x\in [1,6]$ then

asked Dec 23, 2013 by sreemathi.v

1 answer

The value of $\lim\limits_{x\to 0}\large\frac{\int\limits_0^{x^2} \sec^2tdt}{x\sin x}$ is

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

$\lim\limits_{n\to\infty}\large\frac{1+2^4+3^4+......n^4}{n^5}$ - $\lim\limits_{n\to\infty}\large\frac{1+2^3+3^3+......n^3}{n^5}$ =

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

$\lim\limits_{n\to\infty}\large\frac{1^p+2^p+3^p+.....+n^p}{n^{p+1}}$ is

asked Dec 20, 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

$\lim\limits_{x\to 0}\large\frac{\sqrt{1-\cos 2x}}{\sqrt{2x}}$ is

asked Dec 20, 2013 by sreemathi.v

1 answer

If $(x)$ is differentiable and strictly increasing function then the value of $\lim\limits_{x\to 0}\large\frac{f(x^2)-f(x)}{f(x)-f(0)}$ is

asked Dec 20, 2013 by sreemathi.v

1 answer

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