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Recent questions tagged continuity-and-differentiability

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

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

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 $f : R\rightarrow R$ 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

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

Let $f:R\rightarrow R$ be a function defined by $f(x)=max(x,x^3)$.The set of all points where $f(x)$ is not differentiable

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f(x)=x|x|$. The set of points where $f(x)$ is twice differentiable is

asked Dec 20, 2013 by sreemathi.v

1 answer

A discontinuous function $y=f(x)$ satisfying $x^2+y^2=4$ is given by $f(x)$=_________

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f(x)=\left\{\small\begin{array}{1 1} \large\frac{(x^3+x^2-16x+20)}{(x-2)^2}&if\;x\neq 2\\K&if\;x=2\end{array}\right.$. If $f(x)$ is continuous for all $x$ then $K$ =

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f(x)=\left\{\small\begin{array}{1 1}(x-1)^2\sin\large\frac{1}{(x-1)}-\normalsize |x|&ifx\neq 1\\-1&if\;x=1\end{array}\right.$ be a real valued function. Then the set of points where $f(x)$ is not differentiable is

asked Dec 20, 2013 by sreemathi.v

1 answer

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