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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

$\lim\limits_{x\to 1}\big[\sec\big(\large\frac{\pi x}{2}\big)$$\log x\bigg]$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{(1+x)^{1/x}-e}{x}$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0^+}x^m(\log x)^n,(m,n\in N)$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

The value of $\lim\limits_{n\to \infty}x\bigg[\tan^{-1}\large\frac{x+1}{x+2}$$-\cot^{-1}\large\frac{x+2}{x}\bigg]$ is

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

The equation of the plane whose foot of $\perp$ drawn from origin is $(1,2,1)$. is?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane that meets the coordinated axis at the points $A,B,C$ respectively so that the centroid of the $\Delta ABC$ is $(\alpha,\beta,\gamma)$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The direction ratio of the line $3x+1=6y-2,\:z=1$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The point on the line $\overrightarrow r=(-2\hat i-\hat j+3\hat k)+\lambda(3\hat i+2\hat j+2\hat k)$ which is at a distance of $3\sqrt 2$ units from the point $(1,2,3)$ is ?

asked Jan 1, 2014 by rvidyagovindarajan_1

1 answer

The equation of the line through the point $(1,2,3)$ and $\perp$ to the plane $\overrightarrow r.(\hat i+2\hat j-5\hat k)+9=0$ is ?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

The equation of the line through the point $(1,1,3)$ and parallel to the planes $\overrightarrow r.(\hat i-\hat j+2\hat k)=5$ and $\overrightarrow r.(3\hat i+\hat j+\hat k)=6$ is ?

asked Dec 31, 2013 by rvidyagovindarajan_1

1 answer

Integrate: $\int \cos^{-1} (-3x +4x^3)dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \log _a x dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{5-4 \sin x} $$dx$

asked Dec 31, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{\Large\frac{\sqrt 3}{2} \sin x + \cos x }$$dx$

asked Dec 31, 2013 by meena.p

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

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

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

asked Dec 31, 2013 by sreemathi.v

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

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

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

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

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

$f(x)$ 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

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

asked Dec 31, 2013 by sreemathi.v

1 answer

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

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

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

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

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

Integrate : $\int e^x. \bigg[\large\frac{1- \sin x}{1- \cos x }\bigg].$$dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{h\to 0}\large\frac{ln(1+2h)-2ln(1+h)}{h^2}=$

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\bigg[\large\frac{1+5x^2}{1+3x^2}\bigg]^{\Large\frac{1}{x^2}}$

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \sqrt {1+\sin x }dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{\sin ^{-1} x }{(1-x^2)^{3/2}}$$dx$

asked Dec 30, 2013 by meena.p

1 answer

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