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Recent questions tagged limits-continuity-and-differentiability

If $ \sqrt{1-y^2}-\sqrt{1-x^2}=a(x-y),\normalsize$ then find $\large\frac{dy}{dx}$

asked Feb 5, 2014 by rvidyagovindarajan_1

1 answer

If $e^{x+y}=xy,$ what is $\large\frac{dy}{dx}$?

asked Jan 29, 2014 by balaji

1 answer

$\lim\limits_{n\to \infty}\large\frac{1}{n}$$\sum\limits_{r=1}^{2n}\large\frac{r}{\sqrt{n^2+r^2}}$ equals

asked Jan 3, 2014 by sreemathi.v

1 answer

If $f(x)=[x^2]-[x]^2$ where [.] is the largest integer function then

asked Jan 2, 2014 by sreemathi.v

1 answer

If $f(x)=3x^{10}-7x^8+5x^6-21x^3+3x^2-7$ then value of $\lim\limits_{\alpha \to 0}\large\frac{f(1-\alpha)-f(1)}{\alpha^3+3\alpha}$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$f(x)=\sin^{-1}\big(\large\frac{2x}{1+x^2}\big)$ is differentiable on

asked Jan 2, 2014 by sreemathi.v

1 answer

If $\big(\large\frac{2+\sin x}{1+y}\big)\frac{dy}{dx}$$=-\cos x,y(0)=1$ then $y\big(\large\frac{\pi}{2}\big)=$

asked Jan 2, 2014 by sreemathi.v

1 answer

If $\lim\limits_{x\to 0}\large\frac{((a-n)nx-\tan x)\sin nx}{x^2}$$=0$ where $n$ is a non zero real number, then $a$ is equal to

asked Jan 2, 2014 by sreemathi.v

1 answer

Which of the following function is differentiable at $x=0$?

asked Jan 2, 2014 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

$\lim\limits_{x\to\large\frac{-\pi}{4}}\large\frac{1+\tan x}{\cos 2x}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\sin(\pi\cos^2x)}{x^2}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\large\frac{\sqrt{1-\cos 2(x-1)}}{x-1}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

The value of $\lim\limits_{x\to 0}\int\limits_{0^{x^2}}\large\frac{\cos t^2dt}{x\sin x}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\large\frac{x^n}{e^x}$$=0$ for

asked Dec 30, 2013 by sreemathi.v

1 answer

If $G(x)=-\sqrt{25-x^2}$ then $\lim\limits_{x\to 1}\large\frac{G(x)-G(1)}{x-1}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{n\to\infty}\large\frac{n^p\sin^2(n!)}{n+1}$$\qquad0 < p < 1$ is equal to

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}(\log_33x)^{\log_x3}$ is

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 the radius of a sphere is measured as $70$ cm with an error of $0.03$cm, then find the approximate error in calculating its surface area

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

If $y=\tan^{-1}x$, find $\large {\frac{d^2y}{dx^2}}$ in terms of y alone.

asked Jan 2, 2013 by sreemathi.v

1 answer

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