Recently Active Calculus Questions

1) f is a continuous in [a,b] and differentiable in (a,b) wher a>0 such that f(a)/a = f(b)/b prove that der exists x0 e (a,b) such that f'(x0)= f(x0)/x0 2)find the value of a for which f(x)={3x+mod(a2-4) ,a≤x≤1 {5-x2 , ...

\int_{0}^{n\pi}{\left| \frac {sinx}{x}\right|}dx\geq \frac{2}{\pi}(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}) ...

if f:[1,10]→[1,10] is a non decreasing function and g:[1,10]→[1,10] is a non increasing function. let h(x)=f(g(x)) with h(1)=1 the h(2) options 1) lies in (1,2) 2)is more than 2 3)is = to 1 4)is not defined ...

if f(x)= x2/2-2cosx g(x)= x2/6x-6sinx where 0<x<1 find whether f(x) and g(x) r increasing or decreasing function ...

I=\int_{0}^{1}{\frac{dx}{\sqrt{4-x^2-x^3}}};I_1=\int_{0}^{1/2}{\frac{dx}{\sqrt{1-x^4}}} Then find: 1)I 2)I1 3)Imax 4)Imin 5)I1 max 6)I1 min ...

x 2 Sin[x] ∫ -----------------------dx (1 + Cos[x])2 ...

prove that 2/ \pi < sin x/x <1 for x e (0, \pi /2 ) ...

find the values of 'a' for which the function f(x)=(a+2)x3 -ax2+9ax-1 is monotonically decreasing for x eR iknow its very easy but i m not getting the ans i did f'(x)≤0 and afetr taht D<=0 not getting ans with it any oth ...

A : If P(x) is a polynomial of even degree with positive leading coefficient and P(x)-P''(x)≥0 for all xεR then P(x)≥0for all xεR R :lim P(x)= lim P(x)=+∞ x→∞ x→-∞ and min {P(x)} is finite number and at local ...

\int \frac{t(1-t^{2})^{-7/4}}{\sqrt{t+2\sqrt{1-t^{2}}+\sqrt{t+3\sqrt{1-t^{2}}}}}dt ...

Integrate \int \frac{1}{1+\cot x} \ dx ...

Hi T IIT IIANS !!! ...

If y=[tan-1 1/(1+x+x2) + tan-1 1/(x2+3x+3) + tan-1 1/(x2+5x+7) +....] upto n terms,then y'(0) is equal to: a)-1/(n2+1) b)-n2/(n2+1) c)n2/(n2+1) d)none of these ...

integrate ∫sinxcox. complete solution ...

y=f(x) is a function on R->Q and continuous such that f(2)=3.then the function is even/odd/increasing/cant be said. ...

Among various properties of continous, we have if f is continous function on [a,b] and f(a) f(b) < 0, then there exists a point c in (a,b) such that f(x) = 0 equivalently if f is continous on [a,b] and x belongs to R is su ...

\int \frac{e^{kx}}{x}dx btw i required this for a phy q. ...

\int\frac{\sqrt{1-x^{2}}-x}{x^{3}-x^{2}-x+1-\sqrt{1-x^{2}}+x\sqrt{1-x^{2}}}dx It is not as tough as it looks ;) ...

Let f(x) = (a(1-sinx) + bcosx + 5)/x2 if x<0 3 if x=0 (1+(cx+dx3)/x2 )1/x if x>0 If f is continuous at x=0 , then the values of a+b+c is ? A) 2 (B) 0 (C) -4 (D) -5 ...

Which of the following fcns defined below are continuous at the origin ? (A) f(x) = x sin(1/x) if x ≠0 0 if x=0 (B) g(x) = [cos(x2-5x+6)] / (x2 - 5x +6) if x≠2,3 1 if x=2,3 (C) h(x) = xtan-1(1/x) if x≠0 0 if x=0 (D) p(x ...

prove that \int_{0}^{\pi }{}(x^{2}cos x)/(1+sin x)^{2} = (2- \pi )\pi ...

Solve for y... \frac{dy}{dx}=\frac{yf'(x)-y^2}{f(x)} Is not as difficult as it looks?! ...

\frac{d^2y}{dx^2}(x^2+1) = 2x\frac{dy}{dx} Solve for y ...

\int_{0}^{\frac{\pi }{2}}{sec\left(x- \frac{\pi }{6} \right)}sec\left(x-\frac{\pi }{3} \right)dx ...

all these are backlogs... \int \frac{dx}{(1+x^4)^{1/4}} ...

For a sufficiently large value of n the sum of the square roots of the first n positive integers is approximately equal to? ...

Paragraph If f(x) is a differentiable function wherever it is continuous and f '(c1) = f '(c2) = 0, f ''(c1). f ''(c2) < 0, f(c1) = 5, f(c2) = 0 and (c1 < c2) Now answer the following questions, Q. If f(x) is continuous ...

f : [-1, 1] → R. f is continuous and satifies f(2x2 -1) = (x3 + x) f(x) Find f. ...

∫cos8x ...

draw graph of y=sin2x ...