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Recent questions tagged ch5

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

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

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

$f(x)=\large\frac{\log(1+ax)-\log(1-bx)}{x}$ 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

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

Let $f:R\rightarrow R$ be a differentiable function having $f(2)=6,f'(2)=\large\frac{1}{48}$.Then $\lim\limits_{x\to 2}\int_6^{f(x)}\large\frac{4t^3dt}{x-2}$ equals

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

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 $f : R\rightarrow [0,\infty]$ 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

If $( x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} ),$ what is the value of $\frac {\large dy}{\large dx}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

If $x^y\; y^x = 100$, evaluate $\large \frac{dy}{dx}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

If $\;x\sqrt{1+y}+y\sqrt{1+x}=0, \;$ Evaluate $ \large\frac{dy}{dx}$

asked Dec 22, 2013 by balaji.thirumalai

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

For what value of \( \lambda \) is the function defined by \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ \(\leq 0\)}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right.$ What about continuity at \( x = 1\)?

asked Aug 19, 2013 by sreemathi.v

1 answer

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $(iii)\;f (x) = x^2 - 1 \; for\; x \: \in [1,2] $

asked Aug 16, 2013 by sreemathi.v

1 answer

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $ (ii)\;f (x) = [x] \; for\; x \: \in [-2,2]$

asked Aug 16, 2013 by sreemathi.v

1 answer

If $\large\frac{1}{a},\frac{1}{b},\frac{1}{c} $ are in A.P., then the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has

asked Aug 8, 2013 by rvidyagovindarajan_1

1 answer

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