Recently Active Calculus Questions

Not a dbt, If \int_{0}^{\frac{\pi}{2}}{\frac{dx}{a^2cos^2x+b^2sin^2x}}}}=\frac{\pi}{2ab} . Find \int_{0}^{\frac{\pi}{2}}{\frac{dx}{(4cos^2x+9sin^2x)^2}}}} . Quite easy. ...

in the recent past kaymant sir had started numerous threads which has helped many in mean value theorems so can any forum expert start a similar thread on sandwich theorem as due to their experience they wud have come across ...

Prove the following: For every real valued function f differentiable on an interval [a,b] not containing 0 and for all pairs x1 ≠x2 in [a,b], there exists a point ξ in (x1, x2) such that \dfrac{x_1f(x_2)-x_2f(x_1)}{x_1-x_2 ...

Q) Evaluate \int_{0}^{1}{}(tx+1-x)^{n}dx where n is a positive integer and 't' is a parameter independent of 'x' . hence show that \int_{0}^{1}{x^{k}(1-x)^{n-k}}dx=[^{n}C_{k}(n+1)]^{-1} ...

Let f defined on [0,1] be twice differentiable such that |f''(x)|\leq 1 for all x \in [0,1] . If f(0) =f(1) , then show that |f'(x)|<1 for all x \in [0,1] i think such question need mathematically rigorous analysis like th ...

find the maximum product(approximate) of positive real numbers whose sum is 271 and also prove the result. try it very good question and very pretty answer... ...

1. \lim_{n \to \infty} (1 + sin\frac{a}{n})^{n} 2. Function f(x) = (|x - 1| + |x - 2| + cosx), x\epsilon [0,4] is discontinuous at how many points? 3. \lim_{n \to \infty} (\frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} +....+ ...

Suppose f be a continuously differentiable function on [a,b] and twice differentiable at x=a with f''(a) being non-zero; that is, the limit \lim_{x\to a^+}\dfrac{f'(x)-f'(a)}{x-a} exists and is non-zero. Applying LMVT to f in ...

Q1) Prove that if a function f is continuous on [a,b], differentiable on (a,b) and f(a)=f(b)=0, then for any \alpha\in\mathbb{R} , there exists some c\in (a,b) such that \alpha f(c)+f'(c)=0 Q2) Let f and g be functions contin ...

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. ...

range of e^x-[x],x belong to R. ...

Q 1) Prove that f(x)=\frac{x^7}{7}-\frac{x^6}{6}+\frac{x^5}{5}-\frac{x^4}{4}+\frac{x^3}{3}-\frac{x^2}{2}+x-1 has exactly one real root Q 2) In 1 hour a snail travels 60 meters. Prove that there was an Interval of 10 minutes w ...

Find the limit: \lim_{x\to\infty}\left(\sin\sqrt{x+1}-\sin\sqrt{x}\right) (you must supply a proof for your answer.) ...

Let f be a real -valued function with domain R satisfying f(x + 2008) = 1 + 2 - 3f(x) + 3f(x)2 - f(x)3 Answer the following 1) The period of f(x) is a) 2008 b)4016 c) 1004 d) 0 2) The value of f(x+4016) is a) 2008 b) 4016 c)1 ...

If there b a function f(x)=g(x)+h(x), where g(x) is an odd function & h(x) is an even function, then is f(x) an odd or even function? For example, f(x)=sgn(x)+x2 ...

Suppose f is a real valued differentiable function defined on [1,\propto) with f(1)=1 . Given the function satisfies the relation f'(x)=\frac{1}{x^2+f^2(x)} - so now find the maximum value of f(x) for x\ge 1 . ...

Q1)Let g(x) be be function defined on{-1, 1].If the area of the equilateral triangle of two of vertices at(0,0) & (x,g(x)) is 3/4, then the function may be a)g(x)=± (1-x2) b)+ (1-x2) c)- (1-x2) Q2)find domain:f(x)= (sin x) - ...

*Image* [.] denotes the greatest integer function ...

(!) f(x) = Lt n-->∞ [ x/(1+(2sinx)2n) ] then f is discontinuous at (A) pi (B) pi/3 (C) pi/4 (D) pi/6 ...

Let f(x)=\begin{Bmatrix} 1-\left|x \right| & \left| x\right|\leq 1 \\ 0& \left| x\right|\geq 1 \end{Bmatrix} and g(x)=\left| f(x+1)\right|+\left| f(x-1)\right| Number of points where g(x) is discontinuous ? ...

2 \left| sin\frac{\pi x}{3!}\right|-3\left| cos\frac{\pi x }{4!}\right|+tan(\frac{e^{7x}}{e^{[7x]}}+tan\frac{7\pi x}{3}) ...

lim ( n!/(mn)n )1/n n→∞ ...

there was a ques. from gravitation in JEE 2010 m got it some how but wasn't able to integrate it here is the integral i reached *Image* i changed it to x nd y terms........... ...

q1 \lim_{x\rightarrow \infty}[\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}] q2 \lim_{x\rightarrow 0}\frac{e^{tanx}-e^x}{tanx-x} ...

*Image* Please solve ...

maximize, f(x) if, f(x)= tan-1{ (√[2-(x-1)2])/(8-x)} find x for maximum f ;) ...

1. y+x dy/dx = x [f(xy)/f '(xy)], thn f(xy)= ? a) k(e)(x)2/2 b) k(e)(y)2/2 c) k(e)(xy)/2 d) k(e)(xy) 2. y= (c1 +c2)[sin(3x+c3)] - c4e(2x+c5) Find the order of this differential equation: a) 2 b) 3 c) 4 d) 5 ...

1) draw the graph of {x2} ......{.} is fractional part 2) \\If\\\; \theta +\phi =\beta ,\left(0<\beta <\frac{\pi}{2} \right)\\ \textup{then find the max value of} \\ sin^2\theta +sin^2\phi ...

1.Area of the region bounded by the curves x=y2-1 and x=|y| 1-y2 is a.1 b.4/3 c.2/3 d.2 2.A man has 7 relatives 4 of them are ladies and 3 gentlemen ,his wife has also 7 relatives 4 of them are gentlemen and 3 of them are lad ...

Evaluate: \int_{0}^{a}{\frac{ln(1+ax)}{1+x^2}}dx ...