Recently Active Calculus Questions

If\; f(x)=x^{101}+2x^{11}+2x+7\; and\; g(x)\; is\; the\; inverse\; of\; f(x),\; then\; g'(1)\; is?? ...

Plz giv me the rules for integration by the method of substitution. ...

*Image* PLEASE SOLVE THIS 1 ...

Pun in title intended :D This is easy, but good for starters: If f(x+a) = \frac{1+f(x)}{1-f(x)} , prove that f is periodic. ...

if α is the only root of the eqn x3+bx2+cx+1=0(b<c),then the vlaue of tan-1(α) + tan-1(α-1) a)-π/2 b)π/2 c)0 d)none ...

For what values of λ does the function f (x)=(λ+2)x3−3λx2+9λx−1 decrease for all x? ...

let fbe a linear function satisfying f(1)<=f(2) f(3)>=f(4) f(5)=5 then a)f(0)<0 b)f(0)=0 c)f(1)<f(0)<f(-1) d)f(0)=5 ...

∫ln(1+tanx) from o to pi/4 1)pi*ln2/8 2)pi*ln2/4 3)pi*ln2 4)pi*ln4 ...

FIND THE INVERSE OF x+Sinx AND ALSO DRAW THE THE GRAPH OF BOTH THE FUNCTIONS ...

How to differentaite or integrate [x] ????? plzzzz tell fast i forgot [2][2][2] ...

yhe value of ∫1a [x] f'(x) dx, [x] represent greatest integer ...

consider the integral \int_{0}^{inf}{x^{\mu}}dx where μ is real . We have \int_{0}^{inf}{x^{\mu}}dx = \int_{0}^{1}{x^{\mu}}dx + \int_{1}^{inf}{x^{\mu}}dx = I1 + I2 , where I1 is evaluated using the limitng process \lim_{\eps ...

*Image* ...

1.) 0∫Πsin17xcos7x dx 2.) 0∫Π/2 sin8xcos8x dx 3.) 0∫Πsin3x cos6x dx. ...

*Image* Bhaiyyas and Sirs PLEASE let others try first. (Thank You) ...

LIM ( x^n + n(x^(n+1)) + 1 ) / e^[x] x-->∞ [x] = GIF ...

a wire of lenght 20m is bent so as to form a circular sector of maximum area. find the radius of the circular sector and the maximum area ...

∫(x2/(xsinx+cosx)2)dx pls give some hints..... ...

*Image* wer p=natural no≥2 ,a>0 r>0n b≠0 q1 if l eists a)b>1 b)0<b<1 c)b<0 d)b=1 q2if p=3 n l=1 then a= ...

vector A = f '(x) i + g '(x) j vector B = i - f(x) j then: a) A and B are parallel atleast once in (a,b) if g(a) = g(b) b) A and B are perpendicular atleast once in (a,b) if g(a) = g(b) c) A and B are paralle at all x belongi ...

lim_{x\to0}\frac{(1+tan^{-1}3x)^{-3}-(1+sin^{-1}3x)^{-3}}{(1+sin^{-1}2x)^{-2}-(1+tan^{-1}2x)^{-2}} ...

Q If f is a real valued f(x) then f(x) + 2f(2002/x)=3x for all x>0 .Then f(2) (A)1000 (B)2000 (C)3000 (D)4000 ...

please solve this sum..... *Image* ...

*Image* *Image* I M GETTIN ANS AS "C" how bout u ?? ...

I1=∫(x/sinx) int frm 0 to pi/2 I2=∫arc tanx/x int frm 0 to 1 then I1/I2 =? ...

Let polynomials Pn(x) n=0,1,2,3 ...... , be defined by P0(x)=1 P_{n}(x) = \frac{1}{n!}\frac{d^{n}}{dx^{n}}[x^{n}(1-x)^{n}] , n\geq 1 Answer the following Q's 1) The \int_{0}^{1}{P_{n}(x)}x^{k}dx , 0\leq k<n is equla to a) ...

For x>0, \lim_{x\rightarrow 0}\left[(sinx)^{\frac{1}{x}}+\left(\frac{1}{x} \right)^{sinx} \right] is (a) 0 (b) -1 (c) 1 (d) 2 ...

*Image* \int_{-1}^{1}{g'(x)dx} \: = ANS : 2g(1) Wer in the Questn is it Given g(x) is an ODD Functn ??? [7] and widout that HOW CAN g(1) - g(-1) = 2g(1) ??????????????? ...

value of \lim_{n\rightarrow inf}\int_{0}^{1}{\frac{ny^{n-1}}{1+y}}dy single correct A) 1 B) 2 C) 1/2 D) none ...

let the fn f satisfy f(x).f'(-x)=f(-x)f'(x) for all x n f(o)=3 q1the value f(x)f(-x) for all x is a]4 b]9 c]12 d]16 q2 ∫dx/(3+f(x))[limit -51 to 51] a)17 b)34 c)102 d)0 q3 no of roots of f(x)=0 in[-2,2] a1 b0 c2 d4 ...