Recently Active Calculus Questions

$\textbf{Prove that} $\mathbf{\int_{0}^{\frac{\pi}{3}}\ln^2\left(2\sin\frac{x}{2}\right)dx=\frac{7\pi^3}{108}} ...

This is a confusion... \lim_{x\rightarrow 0}\left[\frac{5sinx}{x} \right] = ? \left[. \right] \; is \; gif my vote is 5 . opponent is 4 . what's your vote ? (also explain) ...

1)∫ x2-1/(x2+1)(√x4+1) dx 2)∫sin-1( 2x+2/√(4x2+8x+13) )dx ...

0∫∞ 1/(1+xn)n = 1 find n . ...

is f(x)=x+sinx a strictly increasing or only increasing function ...

∫(1+sinx)/(1+cosx)ex/2dx ...

$\textbf{Determine all function $\mathbf{f:\mathbb{R}\rightarrow\mathbb{R}}$ such that\\\\ $\mathbf{f(x+y)f(x-y)=\left(f(x)+f(y)\right)^2-4x^2f(y)}$,each x,y\in \mathbb{R}$}\\ I have got a quadratic expression. ...

Q- lim [ -2x/tanx ] x→ 0 where [.]=greatest integer function. why isn't the answer -3 ??? ans given is -2 i'm confused at this...... as x→0 tanx/x →1 so x→0 x/tanx →1+ but buk says as x→0 x/tanx < 1 ...

1. If p,q,r are real nos. a. max(p,q)<max(p,q,r) b. min(p,q)=1/2{p+q-mod(p-q)}....mod stands for modulus c. max(p,q)<min(p,q,r) d. none of the above 2.f(x)= cos(x) +cos(√2x) ['x' is not within root] Find the no. of va ...

1.\lim_{x\rightarrow \infty} \frac{\left(\ln x \right)^{2}}{x} NOTE: Without L' Hospital Rule 2.\lim_{x\rightarrow \infty} \left(1+\frac{1}{x} +\frac{1}{x^{2}}\right)^{2x} 3.\lim_{x\rightarrow 1} \left(\frac{x}{x-1} -\frac{1} ...

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We say \lim_{x\rightarrow 2}x^{2}=4 . Let the limit be L . So is L=4 or L<4 or L> 4 ? Having addressed this question, can we conclude on the following statements: 1) \lim_{x\rightarrow 0}\frac{\sin x}{x}=1 \Rightarrow \ ...

i believe we have not discussed this before - prove that epi > pi e. It is not as easy as it luks ! ...

\int_{0}^{\pi }{}e^{cos^{2}x}cos^{3}(2n+1)xdx = ? where n is an integer. I took cos3(2n+1) as a constant. I can't evaluate the remaining integral.Help needed ...

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

generalization of a past jee q Let p(x) be a polynomial over R of even degree n for which for which p(x)≥0 for all x. Prove that p(x) + p'(x) +...+ p(n)(x)≥0 for all x. source :Polynomials, E.J.Barbeau ...

Limitm→∞ Limitn→∞ (1+cos2m(n!πx)) where n! denotes factorial of n.. Answer=2 if x is rational and 1 if x is irrational.. ...

Ltx→0Ltn→∞ 1/n3 ∫nr=1[r2 (sin x)x] ,[x] is greatest integer fn2 ;∫ is summation ...

this sum came in AIEEE 2009.. ∫[cotx]dx from 0 to pi where [.]denotes greatest integer fnctn ...

lt e-1/x/x x→0 ...

i am not able to solve this sum,someone help ∫√tanx dx = ? ...

Let I be an open interval of R. Let f : I--> R be a differentiable functiin such that f does not vanish on I. Prove that f is one-one on I. is the question correct as it stands or instead of f does not vanish on I it shoud ...

find number of maxima and minima of the function whose graph has been drawn *Image* my answer : 1 local minima vote with explanation please.. ...

2x+2| x |≥ 2 2 plz also give me detailed explanation of answer........ ...

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if f(x) = [sin x + cos x] where 0< x < 2∩ [.] = greatest integer function no. of points of discontinuity is ans =5 how to go about??? if we draw the graph using ∩/4 as a unit and get the points of discontinuity is t ...

f(x+y)=f(x)+f(y)....... then show f (x)=xf(1)........for all x..... i got it 4 integer and rational....but how to proove it 4 real?? ...

b^2x^2+a^2y^2=a^2b^2 ...

lim tan2x [ 2sin2x + 3sin x - 4 - sin2x + 6sinx + 2 ] x→∩/2 ...

Let f(x+a) = 1/2 + f(x) - (f(x))2 and 0<=f(x)<=1 Then prove that period of y=f(x) is 2a . ...