# Recently Active Calculus Questions

• Which of the following is an even function? ...
• If f:R o R,, then f(x),=,|x| is ...
• Domain of definition of the function f(x),=frac{3}{4-{{x}^{2}}}+{{log }_{10}}({{x}^{3}}-x),, is ...
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• Let and c be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by ...
• Let f(x+y)=f(x).f(y) and f(x)=1+sin(3x).g(x) where g(x) is cont. , then f'(x) is a) f(x).g(0) b)3g(0) c) f(x).cos(3x) d)3f(x).g(0) e)3f(x).g(x) ...
replied2013-12-23 23:16:58
• If f(x+y)=f(x)f(y) for all x and y and f'(0) exists show that f'(x)=f'(x).f'(0) for all x ...
replied2013-12-23 01:01:16
• 1. If the normal to the curve y= f(x) at x=0 be given by the equation 3x - y + 3 = 0 ,then the value of lim xâ†’0 [x2/{ f(x2) 5 f(4x2) + 4f(7x2)}-1 ] is ???? 2.The tangent to the graph of the function y=f(x) at the point with ...
replied2013-11-24 23:52:06
• *Image* ...
replied2013-11-13 09:14:24
• âˆ«dx/sin2x+tan2x ...
replied2013-11-13 08:15:28
• \hspace{-16}\bf{(1)\;\;}$Total no. of real solution in$\bf{2^x = x^2}$\\\\\\$\bf{(2)\;\;}$Total no. of real solution in$\bf{2^x = 1+x^2}$\\\\\\$\bf{(3)\;\;}$Total no. of real solution in$\bf{2^x+3^x+4^x+5^x = 10x+4}$\ ... replied2013-11-08 06:10:00 • \hspace{-16}\bf{(1)\;\; \int\sqrt{a+\sqrt{b+\sqrt{x}}}\; dx}$\\\\\\ $\bf{(2)\;\;\int \sqrt{1+2\sqrt{x-x^2}}\;dx}$ ...
replied2013-11-07 08:54:53
• \text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
replied2013-11-04 01:12:38
• \hspace{-16}(1)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\sin (kx)\right)^2dx}$\\\\\\$(2)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\cos (kx)\right)^2dx}$\\\\\\ ... asked2013-10-25 11:55:22 • \hspace{-16}\bf{(1)\;\; \int\frac{1}{(1+x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(2)\;\; \int\frac{1}{(1-x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(3)\;\;\int\frac{1}{(1+x^4)}dx}$\\\\\\ $\bf{(4)\;\;\int\frac{1}{(1+x^6)}dx}$ ...
replied2013-10-25 03:34:23
• If f(x) be a positive function in [a,b] prove that, \left|\left(\int\limits^{b}_{a}f(x)dx\right)\left(\int\limits^{b}_{a}\frac{1}{f(x)}dx\right)\right|\geq (b-a)^{2} ...
replied2013-10-06 21:24:10
• \hspace{-16}$If$\bf{\int_{0}^{\infty}\frac{\sin x}{x} = \frac{\pi}{2}\;\; .}$Then value of$\bf{\int_{0}^{\infty}\frac{\sin^3 x}{x^3} = }\$ ...
• âˆ«dx/tanx+cotx+secx+cosecx ...
replied2013-10-01 00:28:41
• 1+x2y2)dx=ydx+xdy ...
replied2013-09-30 23:35:29
• If f(x) is a function which is both even and odd, then f(3) - f(2) is equal to (a) +1 (b) -1 (c) 0 (d) none ...
replied2013-09-30 07:06:17
• *Image* The diagram shows the graph of the derivative of a function y=f(x) for 0<=x<=5 with f(0)=0. âˆ«f(x)dx= [limits from 0 to 1] a.-21/20 b.21/20 c.-1 d.none of these Sir u said option b or d must be correct out of d ...
replied2013-09-28 06:18:42
• Limnâ†’ âˆž [ n2 . âˆ« ( tan-1 nx)/( sin-1 nx) dx Integration upper limit:- ( 1/n ) Integration lower limit:- { (1+ n ) / n } ...
replied2013-09-27 02:20:53
• P.T for any function f(x) and g(x) integrable on the interval (a,b).. \int_{a}^{b}f(x)g(x)dx\leq \sqrt{\int_{a}^{b}f^{2}(x)dx\int_{a}^{b}g^{2}(x)dx} ...
replied2013-09-24 08:50:27
• f(x) = âˆ« 1-sin(2x) then f(Î /4) = ? will it be 2 or 0. because in the sheet that you gave the answer given at the back is (cosx + sinx)sgn(cosx-sinx)+c ...