Recent questions tagged ch5

Is the function $ f(x)=\Large\frac{3x+4\tan x}{x}$ continuous at x = 0? If not, how may the function be defined to make it continuous at this point.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.

asked Jan 25, 2013 by meena.p

1 answer

Given that $ f(x)= \left\{ \begin{array}{1 1} \Large\frac{1- \cos 4x}{x^2}, & \quad if\;x<0 \\ a & \quad ,if\;x=0 \\ \Large\frac{\sqrt x}{\sqrt{16+\sqrt{x}}-4}, & \quad if\;x>0 \end{array}. \right. $ If f(x) is continuous at x = 0, find the value of a.

asked Jan 25, 2013 by meena.p

1 answer

Find $\Large \frac{dy}{dx}$ when $y=\tan^{-1}\Large\frac{1+x^2}{1-x^2}$

asked Jan 25, 2013 by meena.p

1 answer

Find $\Large \frac{dy}{dx}$ when $ y=a^x.x^a$

asked Jan 25, 2013 by meena.p

1 answer

Verify Rolles theorem for the function $f(x)=\sin 2x \;in\;\bigg[0,\Large\frac{\pi}{2}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

Let $y=y=\sqrt{e^\sqrt x },x>0\;find\;\large\frac{dy}{dx}.$

asked Jan 25, 2013 by meena.p

1 answer

If $ f(x)=\begin{vmatrix} x & x^2 & x^3 \\ 1 & 2x & 3x^2 \\ 0 & 2 & 6x \end{vmatrix}$ than find $ f' (x)$

asked Jan 25, 2013 by meena.p

1 answer

If $ f^1(x)=g(x)\;and\;g^1(x)=-f(x)$ for all n and $f(2)=f^1(2)=4,$ find the value of $f^2(24)+g^2(24)$

asked Jan 24, 2013 by meena.p

1 answer

Find the set of all points where the function f(x) = 2x |x| is differentiable.

asked Jan 24, 2013 by meena.p

1 answer

Find $ \frac{dy}{dx}\;when\;y=\Large x^{x^{x^{x.....}}}$

asked Jan 24, 2013 by meena.p

1 answer

Let f be a non zero continuous function satisfying f(x+y) = f(x).f(y) for all x, y $ \epsilon$ R. If f(2) = 9 then find the value of f(3).

asked Jan 24, 2013 by meena.p

1 answer

Let f be continuous function on [1,3]. If f takes only rational values for all x and f(2) = 10 then find the value of f(1.5)

asked Jan 24, 2013 by meena.p

1 answer

True or False: If f.g is continuous at $x=a$,then f and g are separately continuous at $x=a.$

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: The composition of two continuous functions is a continuous function.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f is continuous on its domain D ,then | f | is also continuous on D.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Rolle's theorem is applicable for the function $f(x)=|x-1|$ in [0,2].

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=y(x)$ satisfies $x\cos y + y\cos x = \pi$, then find $y''(0)$:

asked Jan 3, 2013 by sreemathi.v

1 answer

If $f(x)=\mid \cos x-\sin x\mid,then\;f'(\frac{\pi}{3})$=__________.

asked Jan 3, 2013 by sreemathi.v

1 answer

If $f(x)=\mid \cos x\mid$,then $f'(\frac{\pi}{4})$=____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

Derivative of $x^2$ w.r.t $x^3$ is _____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

An example of a function which is continuous everywhere but fails to be differentiable exactly at two point is ____________.

asked Jan 3, 2013 by sreemathi.v

1 answer

For the function $f(x)=x+\large \frac{1}{x},\normalsize x\in[1,3]$,the value of c for mean value theorem is

asked Jan 3, 2013 by sreemathi.v

1 answer

The value of c in Rolle's theorem for the function $f(x)=x^3-3x$ in the interval $[0,\sqrt 3]$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

The derivative of $\cos^{-1}(2x^2-1)$ w.r.t $\cos^{-1}x$ is

asked Jan 3, 2013 by sreemathi.v

1 answer