Recently Active Calculus Questions

Let the range of the function f: R→ R f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 | a being a real parameter given by [α,∞).Then find the no. of integral values of a for which there is exactly one x0ε R such th ...

i,j positive integers f(i,i+1)=1/3(for all i) f(i,j)=f(i,k)+f(k,j)-2f(i,k)(k,j) Find the value of f(1,100) ...

limx→0+ (sin x)sin x = ? ...

∫ Sinx/x =?? ...

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

\hspace{-16}\bf{\int_{0}^{\frac{\pi}{2}}\frac{\sin(2nx).\sin x}{\cos x}dx\;\;, }$ Where $\bf{n\in \mathbb{N}}$ ...

*Image* hw 2 proceed i tried 2 ways 1) took √x=cos2φ... and am stuck at -2tanφsin4φdφ ... 2nd way i tried *Image* and stuck after seperatingthe terms and integrating ...

*Image* *Image* ...

mathop {lim }limits_{x o infty } {left[ {1 + frac{1}{{mx}}} ight]^x} equal to ...

mathop {lim }limits_{x o 0} left( {frac{{{e^x} - 1}}{x}} ight) = ...

int {frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}} dx equals to ...

∫ x+ x2+1 dx HOW TO INTEGRATE?? ...

int_0^{1.5} {[{x^2}]dx} , where [.] denotes the greatest integer function, equals ...

Let a, b, c bc non-zero real numbers such that int_{,0}^{,3} {} (3,a{x^2} + 2,bx + c),,dx = int_{,1}^{,3} {} (3,a{x^2} + 2,bx + c),,dx, then ...

int {frac{{d heta }}{{sin heta ,.,{{cos }^3} heta }}}Â = ...

mathop {lim }limits_{x o 0} frac{{{x^2} - 2x}}{{2sin x}} equals ...

int {{a^x}da = } ...

∫log(x+1) 1/x dx. from 0 to 1. ...

integration of x^2/(a+bx)^2. ...

∫(x2+3)/x6(1+x2)=? Please explain. ...

int{cos 2x.sin 4xdx} equals ...

int {frac{{dx}}{{sin x + sin 2x}}}Â = ...

int {frac{{dx}}{{{{(x - 1)}^2}(x - 2)}}}Â = ...

int {frac{{dx}}{{4{{sin }^2}x + 5{{cos }^2}x}}} ...

∫f(x)/f'(x) dx ...

For real values of x, range of the function y=frac{1}{2-sin 3x} is ...

suppose a,b,n are positive integers , all greater than 1. if an+bn is Prime then what can be said about n ? A) n must be 2 B) n need not be 2 but must be a power of 2 C) n need not be a power of 2 but must be even D) none of ...

\hspace{-16}$If $\bf{f:\mathbb{Z}\rightarrow \mathbb{Z}}$ and $\bf{m + f\big(m + f(n + f(m))\big) = n + f(m)}$\\\\ and $\bf{f(6)=6}$.\;Then $\bf{f(2012)=}$ ...

\hspace{-16}$If $\bf{f:(0,\infty)\rightarrow (1,\infty)}$ and $\bf{f(x)=x^4+x^2+x+1}$. Then $\bf{\frac{d}{dx}\left\{f^{-1}(4)\right\}=}$ ...

If P(x) is a polynomial such that P(x2+1)={P(x)}2+1 and P(0)=0,then ∂P/∂x is equal to: (a)-1 (b)0 (c)1 (d)none of these ...