Recent questions in Mathematics

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

If both the roots of the quadratic equation $(b-c)x^2+(c-a)x+(a-b)=0$ are equal.Then a,b,c are in

asked Dec 31, 2013 by yamini.v

0 answers

Integrate: $\int \large\frac{1}{x \sqrt {x\log (x^2) -5}}$ $dx$

asked Dec 31, 2013 by meena.p

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

If $a^2,b^2,c^2\;$ are in AP , $\frac{1}{b+c},\frac{1}{a+c},\frac{1}{b+a}\;$ are in

asked Dec 31, 2013 by yamini.v

1 answer

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

asked Dec 31, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{1}{4x^2-6x+7}$ $dx$

asked Dec 31, 2013 by meena.p

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

Integrate : $\int \large\frac{1}{\sqrt x -\sqrt {x- 8 }}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

The sum of terms of a series is $\frac{2^n-1}{3}$ .What is the type of series AP or GP. What is the value of d or r (common difference of AP or common ratio of GP)

asked Dec 31, 2013 by yamini.v

1 answer

Integrate: $\int (2x-7) \sqrt {5x+2} dx$

asked Dec 31, 2013 by meena.p

1 answer

Use the formula $\lim\limits_{x\to 0}\large\frac{a^x-1}{x}=$ $ln\; a$ to find $\lim\limits_{x\to 0}\large\frac{2^x-1}{(1+x)^{1/2}-1}$

asked Dec 31, 2013 by sreemathi.v

1 answer

Integrate : $\int \cos ^{-1} \bigg(\large\frac{1-\tan^2 x}{1+\tan^2x}\bigg)$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

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

asked Dec 31, 2013 by sreemathi.v

1 answer

$f(x) =\int \large\frac{x^6+1}{x^2+1}$ $dx+c,$ then find $f(0)-C=?$

asked Dec 31, 2013 by meena.p

1 answer

Find the sum of series 4 + 44 + 444 + 4444 +------upto n terms.

asked Dec 31, 2013 by yamini.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

Integrate : $\int e^x \large\frac{(x+6)}{(x+7)^2}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

In a GP, the ratio of the sum of first 3 terms to the sum of first 6 terms is 125/152. Find the common of the GP.

asked Dec 31, 2013 by yamini.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

Integrate : $\int \large\frac{1}{(\log_ex)^2+1}$

asked Dec 31, 2013 by meena.p

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

Integrate : $\int x^{\tan x }\bigg[\large\frac{\tan x}{x}$ $+ \sec^2 x . \log x \bigg]$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{3x^2+5}{(x^2+1)(x^2+4)}$

asked Dec 31, 2013 by meena.p

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

Integrate : $\int \large\frac{x . \sin x}{1+ \cos x}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

Let $f(a)=g(a)=k$ and their $n^{th}$ derivatives $f^n(a)$ , $g^n(a)$ exist and are not equal for some n. Further if $\lim\limits_{x\to a}\large\frac{f(a)g(x)-f(a)-g(a)f(x)+f(a)}{g(x)-f(x)}$ $=4$ , then the value of k is

asked Dec 31, 2013 by sreemathi.v

1 answer

Integrate : $\int \limits_0^1 (x^3-x^2-x-1) . \sin x dx$

asked Dec 31, 2013 by meena.p

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

Integrate : $\int \limits_0^1 x^4.e^x.dx$

asked Dec 31, 2013 by meena.p

1 answer

$\lim\limits_{x\to \infty}\big[\large\frac{x^2+5x+3}{x^2+x+3}\big]^x$

asked Dec 31, 2013 by sreemathi.v

1 answer

The product of 3 numbers in a GP is 64 and the sum of product of numbers taken in pairs is 56. Find the three numbers in GP.

asked Dec 31, 2013 by yamini.v

1 answer

Integrate : $\int \large\frac{3x}{(x+1)(x+2)}$ $dx$

asked Dec 31, 2013 by meena.p

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 $f:R\rightarrow R$ be such that $f(1)=3$ and $f'(1)=6$ . Then $\lim\limits_{x\to 0}\big[\large\frac{f(1+x)}{f(1)}\big]^{\Large\frac{1}{x}}$ equals

asked Dec 31, 2013 by sreemathi.v

1 answer

If 4 positive numbers a, b, c and d are in HP, which of the following is true.

asked Dec 31, 2013 by yamini.v

1 answer

Integrate : $\int \large\frac{dx}{(x-p) \sqrt {(x-p)} \sqrt {x-q}}$

asked Dec 31, 2013 by meena.p

1 answer

The left hand derivative of $f(x)=[x]\sin(\pi x)$ at $x=k$ , where $k$ is an integer is

asked Dec 31, 2013 by sreemathi.v

1 answer

Given that $\frac{S_{1}}{S_{2}}=\frac{3n+8}{7n+5}$ , $\frac{S_{1}}{S_{2}}$ is the ratio of sum of two APs to n terms, find the ratio of the 11<sup>th</sup> terms of the two APs.

asked Dec 31, 2013 by yamini.v

1 answer

Integrate : $\int \large\frac{\cos x - \sin x}{\sqrt {\sin 2x}}$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

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

asked Dec 31, 2013 by sreemathi.v

1 answer

Find the sum of the series -1 + 4 - 9 + 16 - 25 +-----+ 4008004.

asked Dec 31, 2013 by yamini.v

1 answer

Integrate : $\int \large\frac{3}{7} .\frac{2^{\Large \log e^{x^2}}}{x}.$ $dx$

asked Dec 31, 2013 by meena.p

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

Integrate : $\int \large\frac{\cos^2 x}{\sin ^4 x }$ $dx$

asked Dec 31, 2013 by meena.p

1 answer

If $f(x)=\left\{\begin{array}{1 1}\large\frac{\sin [x]}{[x]}&[x]\neq 0\\0&[x]=0\end{array}\right.$ , where $[x]$ denotes the greatest integer less than or equal to x, then $\lim\limits_{x\to 0}f(x)$ equals

asked Dec 31, 2013 by sreemathi.v

1 answer

If $f(a)=2$ , $f'(a)=1$ , $g(a)=-1$ , $g'(a)=2$ , then the value of $\lim\limits_{x\to a}\large\frac{g(x)f(a)-g(a)f(x)}{x-a}$ 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

Find the sum of the series $1^2$ - $2^2$ + $3^2$ - $4^2$ + $5^2$ - $6^2$ ..... $1000^2$ .

asked Dec 31, 2013 by yamini.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

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