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) ...

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 ...

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 x→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 ...

*Image* ...

∫dx/sin2x+tan2x ...

\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 $\bf{2^x+3^x+4^x+5^x = 10x+4}$\ ...

\hspace{-16}\bf{(1)\;\; \int\sqrt{a+\sqrt{b+\sqrt{x}}}\; dx}$\\\\\\ $\bf{(2)\;\;\int \sqrt{1+2\sqrt{x-x^2}}\;dx}$ ...

\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)\ \ ...

\hspace{-16}(1)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\sin (kx)\right)^2dx}$\\\\\\ $(2)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\cos (kx)\right)^2dx}$\\\\\\ ...

\hspace{-16}\bf{(1)\;\; \int\frac{1}{(1+x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(2)\;\; \int\frac{1}{(1-x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(3)\;\;\int\frac{1}{(1+x^4)}dx}$\\\\\\ $\bf{(4)\;\;\int\frac{1}{(1+x^6)}dx}$ ...

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} ...

\hspace{-16}$If $\bf{\int_{0}^{\infty}\frac{\sin x}{x} = \frac{\pi}{2}\;\; .}$ Then value of $\bf{\int_{0}^{\infty}\frac{\sin^3 x}{x^3} = }$ ...

∫dx/tanx+cotx+secx+cosecx ...

1+x2y2)dx=ydx+xdy ...

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 ...

*Image* The diagram shows the graph of the derivative of a function y=f(x) for 0<=x<=5 with f(0)=0. ∫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 ...

Limn→ ∞ [ n2 . ∫ ( tan-1 nx)/( sin-1 nx) dx Integration upper limit:- ( 1/n ) Integration lower limit:- { (1+ n ) / n } ...

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} ...

f(x) = ∫ 1-sin(2x) then f(Π/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 ...

\bf{\int\frac{1}{(x^2-x+1)\sqrt{x^2+x+1}}dx} ...

∫ dx/sec2x + tan2x ...

Form the differential equation corresponding to y2-2ay+x2=a2 ...

if f(xy)=f(x)f(y) for all x and y and f(x)is continuous at x=1 ,prove that f(x)is continuous at all non zero x. ...

If Im,n = ∫cosmx.sin(nx).dx, then find 7I4,3 - 4I3,2. ...

Among all cyclic quadrilaterals inscribed in a circle of radius R with one of its angles equal to 120°, consider the one with maximum possible area. Its area is: (a) √2R2 (b) 2R2 (c) √3R2 (d) 2√3R2 ...