Recently Active Calculus Questions

value of f(0), so that its function f(x)=( 1+2x - 1+2x )/x is continues is a)1/3 b)3 c)-1/3 d)0 ...

If f(x)=[x2]-[x]2 and x lies between [0,2] then the range of f(x) is: (a){-1,0} (b){-1,0,1} (c){0} (d){0,1,2} ...

sin ax+cos ax and |sin x|+|cos x| are periodic functions of same fundamental period then a is: (a)0 (b)1 (c)2 (d)4 ...

\ cos4xcos7x =\ 1/2(cos3x+cos11)dx where'\' is sign of integration. is there any formulae regarding to it... ...

IF y=x+x2/2+x3/3+x4/4+....... THEN PROVE THAT x=y-y2/2!+y3/3!+y4/4!+....... ...

\hspace{-16}\mathbb{I}$f $\bf{n=\frac{1}{\frac{1}{1980}+\frac{1}{1981}+........+\frac{1}{2012}}}$. Then $\bf{\lfloor n \rfloor}$ is \\\\\\ Where $\bf{\lfloor x \rfloor = }$Floor Sum. ...

1) ∫√secx ...

If f(x)= cos nx sin 5x/n is periodic with peiod 3Ï€ then find the sum of integral values of n. ...

\hspace{-16}$If $\bf{f(x+1)=(-1)^{x+1}.x-2f(x)\forall x\in \mathbb{N}}$ and $\bf{f(1)=f(1986)}$\\\\ Then Sum of Digit of the no. $\bf{f(1)+f(2)+f(3)+.....+f(1985)}$ ...

∂n/∂xn(log x) is: (a)(n-1)!/xn (a)(n)!/xn (a)(n-2)!/xn (a)(-1)(n-1)(n-1)!/xn ...

In many books a shortcut trick for checking differnetiabiltiy of a fuction is given by first differentiate LHS and RhS and check if both the slope are coming same, provided the function is continous. However in many question ...

1. ∫tan7 x/2 sec2 x/2 dx 2.∫ x + 2/(1 + x )2 dx Plz Help ...

\hspace{-16}\bf{\int\tan^{2}(x).\sin^{-1}(\tan x-x)dx} ...

if f(x - 1) + f(x + 1) = √3 f(x) then prove that f(x) is periodic with period 12` ...

Please integrate ∫(x^2 + 1)/(x^4+x^2+1) dx ...

my question is in solving a equation say f(x)=g(x) graphically if it happens that I am confused that whether the graph of f(x) really intersects a point or not ...how to get rid of that confusion?? ...

Show that infinete series Σ sin( 1/k ) is div? ...

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1) tan3x +cos (2.5x) 2) cos(cosx) + cos(sinx) ...

\hspace{-16}\bf{\mathbb{F}}$ind a function $\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$ that satisfy\\\\\\ $\bf{2f(x)+f(-x)=\left\{\begin{matrix} \bf{-x^3-3}\;\;\;,\;x\leq 1\\\\ \bf{7-x^3}\;\;\;,\;x> 1 \end{matrix}\right.}$ ...

What will be the graph of (Sinx)/x ? ...

What will be the graph of (Sinx)/x ? ...

\hspace{-16}\bf{\mathbb{S}}$olve for $\bf{x}$\\\\ $\bf{(1)\;\; \lfloor 1.5 \rfloor x+\lfloor x \rfloor=5}$\\\\ $\bf{(2)\;\; \lfloor x \rfloor+\lfloor 2x \rfloor \leq \sqrt{3}}$ ...

∫√x+√x2+2.dx plz help me out to solve dis one ...

\hspace{-16}\bf{\left\lfloor \dfrac{10^{20000}}{3+10^{100}}\right\rfloor=}$\\\\\\ Where $\bf{\lfloor x \rfloor =}$ Floor Function. ...

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1. INTEGRATE A)∫dx/x22(x7-6) B)∫dx/(x+3)8/7(x-2)6/7 C) ∫(lnx-1)/((lnx)2-1)dx ...

\hspace{-16}$If $\bf{\mathbb{I}=\int_{0}^{\pi}\frac{\sin(884\;x).\sin(1122\;x)}{\sin (x)}dx}$ and $\bf{\mathbb{J}=\int_{0}^{1}\frac{x^{238}.(x^{1768}-1)}{(x^2-1)}dx}$\\\\\\ Then value of $\bf{\frac{\mathbb{I}}{\mathbb{J}}=}$ ...

Given: f(x) =ax2+bx+c g(x)= px2+qx+r such that f(1)=g(1), f(2)=g(2) and f(3)-g(3) = 2 . Find f(4)-g(4). The q is easy but i want a shorter method... ...

I=∫ 6x3+x2-2x+1/2x-1 . Integrate this function. ...