Popular Calculus Questions

Q) If y= cosx+ cosx+ cosx ...... Prove that (2y-1)dy/dx+sinx=0. ...

Find Lim x----->0+ for the function f(x)= *Image* ...

\int \sqrt{(x^4 + 1)/ (x^2 + 1) } ∂x ......................... (AKAND NE KAHA ISLYE) is this integrable????? IF YES, HOW?????? GIV DA FINAL ANS THEN........ ...

LIMITs *Image* ...

Find the area bounded by r=a(1+cosθ),0<θ<2π. ...

Find the area under one loop of r=acos4θ ...

find the smallest area by y=f(x), when f(x) is a polynomial of least degree satisfying lim(x->0) [1+(f(x)/x^3)]^(1/x)=e, and the circle x^2+y^2=2 above the x-axis. ...

∫03 (x2+1)d([x]). [.]→ G.I.F. ...

Find \lim_{n\rightarrow \infty}\int_{0}^{1}{}x^{2}e^{-(\frac{x^2}{n^2})}dx ...

\lim_{x\rightarrow \propto } [ 1^{1}+2^{1/2} + 3^{1/3} + ...... + x^{1/x} ] ...

if a continous function satisfies F(F(x))=1/F(x) and F(1000)=999, Find F(500) ...

f is a real valued infinitely differentiable function.f(0) = 0 and f"(x) >0 for all real x then f(x)/x is 1) increasing on (0,∞) 2) increasing on (-∞,∞) 3)decreasing on (0,∞) 3)decreasing on (-∞,∞) ...

∫pi0 1/1+tanx dx ...

let be a real valued function satisfying f:[a,b]\rightarrow [a,b] \\ a,b \in \mathrm{R} 1)continous in [a,b] f^2(a)-f^2(b)=a^2-b^2 prove that f(x).f'(x)=x for some x \in [a,b] P.S. RICKY IS PROHIBTIED FROM ANSWERING ...

lim x→0 [(sin signum(x))/signum(x)] where [] is GIF?? options are given (a)0 (b)1 (c)1/2 (d) does nt exsist Q2 Let {x} denote the fractional part of x then lim x→0 ({x})/tan({x}) is equal to=?? Q3. lim x→0 (1-cos(1-cosx ...

*Image* ...

Let f(x)=(x2+4x)1/3 and let g(x) be an antiderivative of f(x). Then if g(5) = 7 find g(1) ...

Which is greater in the following pairs? (i) e^\pi or \pi^e (that's old) (ii) 2^{\sqrt{2}} or e (iii) \ln 8 or 2. In each case your answer must be accompanied by a proof. ...

f(x)=sin x + x ; find ∫0pi f-1(x) dx. ...

draw the graph of sin(ex) ...

limx→π/2 (sinx - sinxsinx)/(1-sinx+lnsinx) ...

1) Find \lim_{x\rightarrow0}{{\left( \frac{1^{x}+2^{x}+3^{x}+.....+n^{x}}{n}\right)^{1/x}}} 2) Find \lim_{n\rightarrow(infinity)}\frac{1^{k}+2^{k}+3^{k}+........+n^{k}}{n^{k+1}} ...

If ax2 - bx + c = 0 have two distinct roots lying in the interval (0,1), a, b, c ε N, then prove that log5(abc) ≥ 2. ...

sininverse((2x+2/( 4x2+8x+13 ))) ...

Again from Askiitians.com (this problem was an oasis in the mind-numbingly boring queries there) Find all continuous functions f: R→R satisfying f[(x-y)2] = f2(x) - 2x f(y) + y2 ...

f(1/x)+x2f(x)=0 for all x>0 and I=\int_{1/x}^{x}{f(z)dz} 1/2<=x<2 i did like this f(1/x)+x2f(x)=0 ----------(1) replace x by 1/x =>f(x)+1/x2 f(1/x)=0 Now dI/dx=f(x).1 -(-1/x2 f(1/x))=> dI/dx=f(x)+1/x2 f(1/x) dI ...

To add to the action already taking place in this forum: Prove that e^x\geq 1+x\quad\forall \,x\in\mathbb{R} , the set of real numbers (easy part.) Using this result, prove the Arithmetic Mean - Geometric Mean inequality for ...

Solve :- \int \left(a-x \right)\left(b-x \right)\left(c-x \right)...............\left(z-x \right)dx ...

What is the value of limn→∞Πn=0n(1+1/22n)?? ...

ƒ : R → R is a twice diffentiable fn. such that ƒ'(x) = ƒ(1-x) for all x \epsilon R Given ƒ(0) = 1 , Find ƒ(1) (A) e - 2 (B) ln 2 - 1 (C) sec 1 + tan 1 (D) cos 1 + sin 1 ...