Recently Active Calculus Questions

f(x) be a continous and differentiable function. f(y)f(x+y)= f(x) f(5) = 3 and f'(3)=7 then f'(8) = ........ ...

Evaluate \int_1^e\dfrac{1+x^2\ln x}{x+x^2\ln x}\ \mathrm dx ...

Draw graph of y={x}+2{2x}+4{4x} [1][1] ...

domain of 1) log0.3(x-1)/x2-2x-8 2)cos -1( 1-2lxl/3 ) just give ur ans...no soln needed ...

prove \mathbf{}\int_{0}^{infinity}{sinx.dx}=1 ...

draw the graph of eesin x ...

draw graph of esin x ...

Number of solns for x between 3 and 15 if \int_{0}^{x}{\left[t \right]}.dt=\int_{0}^{\left[x \right]}{t.dt} wer [.] is GIF ...

Given a function f : [0,4] ----> R is differentiable , then for some \alpha , *Image* \epsilon (0 , 2) , \int_{0}^{4}{f(t) dt} equals to : a) f( \alpha 2) + f( *Image* 2) b)2 \alpha f( *Image* 2) + 2 *Image* f( \alpha 2) c ...

FROM A FIXED POINT a ON THE CIRCUMFERENCE OF A CIRCLE OF RADIUS r THE PERPENDICULAR "AY" IS LET FALL ON THE TANGENT AT P . THE MAXIMUM AREA OF TRIANGLE APY IS: A) r2 B) 2√3 r2/4 C) 3√3 r2/4 D) √3 r2 ...

A compilation of quesitons similar to the way bhargav had one :P (hence borrowed a part of the name..) Keep solving and i will keep adding questions here... To begin with first 5 are here... Question 1) \left(\frac{dy}{dx}+1\ ...

x \int \frac{\sqrt{2sin ( x ^ 2-1 ) - sin 2( x^2 -1 )}}{ \sqrt{2sin ( x^2 -1)+ sin2 ( x^2 -1 )} }where x^2 -1 \neq n\pi ans is log \mid \left( sec \frac{ x^2 -1 }{2} \right) \mid + c for practice ...

\int \frac{dx}{(1+\sqrt{x})(\sqrt{x + x^{2}})} ans is. \sqrt{2}log tan \left\{\frac{1}{2}(tan^{-1}\sqrt{x})+\frac{\pi }{8} \right\} + c ...

The smaller area enclosed by y = f(x) when f(x) is polynomial of least degree satisfying *Image* 1/x = e and the circle x2 + y2 = 2 above the x axis is a) \pi / 2 b) 3/5 c) \pi /2 - 3/5 d) \pi /2 + 3/5 ...

1..if f:R→R be a differential finction such that that f(2-x)=f(x) and f(5-x)=f(5+x) then 1.f'(-3)=0 2..f'(9)=0 . 3.if \int_{3}^{5}{f(x)dx=k},then \int_{11}^{15}{f(x) dx} wil l be k ...

area of the region bounded by the curve *Image* is A) 3 sq . unit B) 4 sq . unit C) 1 sq . unit D) 2 sq . unit ...

Prove (1 - cos A) /(sin A) tan(A/2) ...

*Image* ...

how to draw graph of x^(something in fraction) say x2/3 ...

f(x)=a_0+a_1cosx+a_2cos2x+a_3cos3x+...+a_ncosnx g(x)=b_1sinx+b_2sn2x+b_3sin3x+..+b_nsinnx Q1 If br= 1/r+1 ,then \lim_{n\rightarrow \infty} \int_{0}^{\pi }{g(x)dx} Q2 \sum_{k=0}^{n}{\int_{0}^{2\pi }{f(x).(cos kx)dx}} Q3 \sum_{ ...

\int {e^{x\sin x+\cos x}}\left(\frac{x^4\cos^3x-x\sin x +\cos x}{x^2\cos^2 x} \right)dx ...

\int_{0}^{\frac{\pi }{2}}{\frac{sec^{2}x}{(secx+tanx)^{n}}}dx,n>1 ...

Q1 If f(x)= {x}g(x)/{x}g(x) is a periodic fn with pd 1/4 where g(x) is diff fn. then prove g(x)=0 at x=k/4 k ε I Q2 f: R→R,f(x)= x2+bx+1/x2+2x+b ,if the function f(x) and 1/f(x) have same bounded set as their range then fi ...

\int_{0}^{2a}{\sqrt{2ax-x^{2}}}dx ...

\int \frac{dx}{\sqrt{1-\sqrt{x}}} ...

If I_{n}=\int_{-\pi }^{\pi }{\frac{sin (nx)}{(1 + \pi ^{x})sin x}}dx, n = 0,1,2.... then A) I_{n} = I_{n+2} B) \sum_{m=1}^{10}{I_{2m+1}} = 10\pi C) \sum_{m=1}^{10}{I_{2m}} = 0 D) I_{n} = I_{n+1} (MULTIPLE OPTIONS CORRECT) ...

find \int_{0}^{\pi/4}{\frac{x dx}{cosx(cosx +sinx)}} ...

1..∫ X2/(A+BX)2 dx ...

EVALUATE *Image* ...

\lim_{n\rightarrow \infty}\frac{(\sum_{x=1}^{n}{x^4})(\sum_{x=1}^{n}{x^5})}{(\sum_{x=1}^{n}{x^t})(\sum_{x=1}^{n}{x^{9-t}})}=\frac{4}{5} ...