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Recent questions tagged continuity-and-differentiability

If $ f(x) = \left\{ \begin{array}{l l} \large\frac{x^3+x^2-16x+20}{(x-2)^2} & \quad when \quad x \neq 3 \\ k & \quad when \quad x = 2 \end{array} \right. $ and $f(x)$ is continuous at $x=3$ find the value of k.

asked Apr 22, 2014 by meena.p

1 answer

If $ f(x) = \left\{ \begin{array}{l l} \large\frac{|x+2|}{\tan^{-1} (x+2)} & \quad x \neq -2 \\ 2 & \quad x=-2 \end{array} \right. $ then $f(x) $ is

asked Apr 22, 2014 by meena.p

1 answer

If the function $ f(x) = \left\{ \begin{array}{l l} 3ax+b & \quad for \quad x > 1 \\ 11 & \quad for \quad x = 1 \\ 5ax-2b & \quad for \quad x < 1 \end{array} \right. $ is continuous at $x=1$.find the values of a and b .

asked Apr 22, 2014 by meena.p

1 answer

Find the values of K. So that the function $ f(x) = \left\{ \begin{array}{l l} \large\frac{k \cos x}{\pi -2x} & \quad if \quad x \neq \large\frac{\pi}{2} \\ 3 & \quad if \quad x =\large\frac{\pi}{2} \end{array} \right. $ is continuous at $x =\large\frac{\pi}{2}$ .

asked Apr 22, 2014 by meena.p

1 answer

Determine the value of K so that the function. $ f(x) = \left\{ \begin{array}{l l} Kx^2 & \quad if \quad x \leq 2 \\ 3 & \quad if \quad x > 2 \end{array} \right. $ is continuous .

asked Apr 22, 2014 by meena.p

1 answer

The set of points where the function $f(x)=\sqrt{1-e^{-x^2}}$ is differentiable is

asked Jan 6, 2014 by sreemathi.v

1 answer

At the point $x=1$ the function $f(x)=\left\{\begin{array}{1 1}x^3-1&1 < x < \infty\\x-1&-\infty < x \leq 1\end{array}\right.$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

$f(x)=\left\{\begin{array}{1 1}\large\frac{1-\cos 4x}{x^2}&x < 0\\a&x=0\\\large\frac{\sqrt x}{\sqrt{[16+\sqrt x]-4}}&x > 0\end{array}\right.$If the function be continuous at $x=0$ then $a=$

asked Jan 6, 2014 by sreemathi.v

1 answer

The function $f(x)=\left\{\begin{array}{1 1}x+a\sqrt 2\sin x&0\leq x < \large\frac{\pi}{4}\\2x\cot x+b&\large\frac{\pi}{4}\normalsize \leq x < \frac{\pi}{2}\\a\cos 2x-b\sin x&\large\frac{\pi}{2}\normalsize < x \leq \pi\end{array}\right.$ is continuous for $0 \leq x \leq \pi$ then a,b are

asked Jan 6, 2014 by sreemathi.v

1 answer

The function $f(x)=\left\{\begin{array}{1 1}\large\frac{x^2}{a}&0\leq x <1\\a&1\leq x < \sqrt 2\\\large\frac{2b^2-4b}{x^2}&\sqrt 2\leq x < \infty\end{array}\right.$ is continuous for $0\leq x < \infty$ then the most suitable values of a and b are

asked Jan 4, 2014 by sreemathi.v

1 answer

The value of $\lim\limits_{x\to 0}\large\frac{\sqrt{\Large\frac{1}{2}\normalsize (1-\cos 2x)}}{x}$

asked Jan 4, 2014 by sreemathi.v

1 answer

If $f(x)=\large\frac{x}{2}$$-1$, then on the interval $[0,\pi]$

asked Jan 4, 2014 by sreemathi.v

1 answer

The set of all points where the function $f(x)=\large\frac{x}{(1+|x|)}$ is differentiable is

asked Jan 4, 2014 by sreemathi.v

1 answer

Let $[x]$ denote the greatest integer less than or equal to x. If $f(x)=[x\sin\pi x]$, then $f(x)$ is

asked Jan 3, 2014 by sreemathi.v

1 answer

If $f(x)=x(\sqrt{x}-\sqrt{x+1})$ then

asked Jan 3, 2014 by sreemathi.v

1 answer

If $x+|y|=2y$, then $y$ as a function of x is

asked Jan 3, 2014 by sreemathi.v

1 answer

Consider the function $f(x)=|x-2|+|x-5|\;x\in R$.

asked Jan 3, 2014 by sreemathi.v

1 answer

If $f:R\to R$ is a function defined by $f(x)=[x]\cos\big(\large\frac{2x-1}{2}\big)$$\pi$ where [x] denotes the greatest integer function then f is

asked Jan 3, 2014 by sreemathi.v

1 answer

Let $f(x)=[x]\sin\bigg[\large\frac{\pi}{[x+1]}\bigg]$ where [.] denotes the greatest integer function. The domain of $f$ is and the point of discontinuity of $f$ in the domain are

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f(x)$ = $(x^2-1)\;$ $|x^2-3x+2|$ + $\cos(|x|)$ is not differentiable at

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f(x)=[x]^2-[x^2]$ where $[x]$ is the greatest integer less than or equal to x, is discontinuous at

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f:R\{0\}\rightarrow R$ given by $f(x)=\large\frac{1}{x}-\frac{2}{e^{2x}-1}$ can be made continuous at $x=0$ by defining f(0) as

asked Jan 3, 2014 by sreemathi.v

1 answer

$f$ is defined in [-5,5] as $f(x)=\left\{\begin{array}{1 1}x&if\;x\;is\;rational\\-x&if\;x\;is\;irrational\end{array}\right.$. Then

asked Jan 3, 2014 by sreemathi.v

1 answer

The function given by $y=||x|-1|$ is differentiable for all real numbers except the points

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f(x)=[x]\cos\big[\large\frac{2x-1}{2}\big]$$\pi$ where [.] denotes the greatest integer function, is discontinuous at

asked Jan 3, 2014 by sreemathi.v

1 answer

In order that the function $f(x)=(x+1)^{\large\cot x}$ is continuous at $x=0$. f(0) must be defined as

asked Jan 2, 2014 by sreemathi.v

1 answer

If $f$ is twice differentiable and $f''(0)=2$ then $\lim\limits_{x\to 0}\large\frac{2f(x)-3f(2x)+f(4x)}{x^2}$=

asked Jan 2, 2014 by sreemathi.v

1 answer

If $f(x)=\left\{\begin{array}{1 1}\large\frac{1-\cos\lambda x}{x\sin x}&x\neq 0\\\large\frac{1}{2}&x=0\end{array}\right.$ is continuous at $x=0$ then $\lambda$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

Find the value of p for which the function $f(x)=\left\{\begin{array}{ 1 1}\large\frac{(4^x-1)^3}{\sin\big(x/p\big)\log \big(1+\Large\frac{x^2}{3}\big)}&x\neq 0\\12(\log 4)^3&x=0\end{array}\right.$ is continuous at $x=0$

asked Dec 31, 2013 by sreemathi.v

1 answer

Find the points of discontinuity of $y=\large\frac{1}{u^2+u-2}$ where $u=\large\frac{1}{x-1}$

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a function such that $f(x+y)=f(x)+f(y)\forall x,y\in R$ if $f(x)$ is differentiable at $x=0$ then

asked Dec 31, 2013 by sreemathi.v

1 answer

The values of $p$ and $q$ for which the function $f(x)=\left\{\begin{array}{1 1}\large\frac{\sin(p+1)x+\sin x}{x} & x < 0 \\ q & x=0 \\ \large\frac{\sqrt{x+x^2}-\sqrt x}{x^3/2} & x > 0 \end{array}\right.$ is continuous for all $x\;in\;R$ are

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a function defined by $f(x)=min\{x+1,\mid x\mid+1\}$. Then which of the following is true ?

asked Dec 31, 2013 by sreemathi.v

1 answer

If $f$ is a real valued differentiable function satisfying $\mid f(x)-f(y)\mid\leq (x-y)^2,x,y\in R$ and $f(0)=0$ then $f(1)$ equals

asked Dec 31, 2013 by sreemathi.v

1 answer

$f(x)$ and $g(x)$ are two differentiable function on [0,2] such that $f''(x)-g''(x)=0$. $f'(1)=2g'(1)=4f(2)=3g(2)=9$ then $f(x)-g(x)$ at $x=\large\frac{3}{2}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

If $f(x)$ is continuous and differentiable function and $f(1/n)=0\forall n \geq 1$ and $n\in 1$ then

asked Dec 31, 2013 by sreemathi.v

1 answer

Let [.] denote the greatest integer function and $f(x)=[\tan^2x]$ then

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a differentiable function and $f(1)=4$, then the value of $\large \int_4^{f(x)}\large\frac{2t\;dt}{x-1}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function $f(x)=\large\frac{\tan(\pi[x-\pi])}{1+[x]^2}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f(x)$ be a continuous function defined for $1\leq x\leq 3$. If $f(x)$ takes rational value for all $x$ and $f(2) = 10$ then $f(1.5)$ =

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f(x)=\left\{\begin{array}{1 1}\big[\tan(\large\frac{\pi}{4}\normalsize +x)\big]^{\large\frac{1}{x}}&x\neq 0\\k&x=0\end{array}\right.$.For what value of k,$f(x)$ is continuous at $x=0$

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f(x)=\large\frac{1}{1-x}$,find the points of discontinuity of the composite function $y=f(f(f(x)))$

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f(x)=\large\frac{x^2-10x+25}{x^2-7x+10}$ for $x\neq 5$ and $f$ is continuous at $x=5$ then $f(5)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

$f(x)=\left\{\begin{array}{1 1}\large\frac{x^5-32}{x-2}&x\neq 2\\k&x=2\end{array}\right.$ is continuous at $x=2$ then $k=$

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f$ is continuous on $[0,1]$ and $f\big(\large\frac{1}{3}\big)$$=1$ then $\lim\limits_{n\to \infty}f(\large\frac{n}{\sqrt{9n^2+1}}\big)$=

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\log (x+y)=2xy$ then $y'(0)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f(x)=\large\frac{1-\tan x}{4x-\pi}\qquad $$x\neq \large\frac{\pi}{4}$,$x \in [0,\large\frac{\pi}{2}]$ and f(x) is continuous in $[0,\large\frac{\pi}{2}]$ then $f(\large\frac{\pi}{4})$

asked Dec 24, 2013 by sreemathi.v

1 answer

The number of points at which the function $f(x)=\large\frac{1}{\log|x|}$ is discontinuous is

asked Dec 24, 2013 by sreemathi.v

1 answer

The value of $f(0)$ so that the function $f(x)=\large\frac{2x-\sin^{-1}x}{2x+\tan^{-1}x}$ is continuous at each point on its domain is

asked Dec 24, 2013 by sreemathi.v

1 answer

If the function $f(x)=\left\{\begin{array}{1 1}\large\frac{x^2-(A+2)x+A}{x-2}&x\neq 2\\2&x=2\end{array}\right.$ is continuous at $x=2$ then

asked Dec 24, 2013 by sreemathi.v

1 answer

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