Recently Active Calculus Questions

if a force is applied to top of a cube from one side of lngth L with mass m and frictn co-eff btwn floor and cube surface is φ find the minimum force to turn the cube the other side without allowing cube to slip ...

if Σn=55 , then Σn2= ...

\hspace{-16}\bf{\int_{0}^{1}x^{2012}.(1-x)^{2012}dx} ...

\hspace{-16}\bf{\int_{0}^{1}\frac{x(x+1).e^x}{x+1+e^x}dx} ...

\hspace{-16}\bf{\int_{-3}^{3}x^8.\left\{x^{11}\right\}dx=}$\\\\\\ Where $\bf{\{x\}=}$ Fractional Part function......... ...

how to solve foll integration please give detail soln ::; 1)) ∫ dx 4sin2x+4sinxcosx+5cos2x if xε(-Π/2,Π/2) 2))x ∫ 2t dt 0 2[t] x>0 [] is g.i.f ...

integer type::::: 1) let f(x)=k/2009 and g(x)= f4(k) (1-f(k))4 + (f(k))4 then sum of digits in the value of *Image* is 2) if S=1/2+1/6(12+22)+1/12(12+22+32)+.............+ 1/3660(12+22+32+................602) then sum of digi ...

Question: f(x)=(2x-∩)3 +2x - cosx. Then the value of |f'(f-1(x))| at x=∩ is _______? answer: 1/3 I think drawing the graph is only way. Any accurate and easier solution please tell me. (SOURCE: ARIHANT) ...

for the principal value of sin-1(sin5)+cos-1(cos6)+tan-1(tan7)=k-2Ï€ find the integral value of k it is silly b ut its a doubt...... ...

Let x={a1,a2,a3,......,a6} and y={b1,b2,b3}. Then number of functions f from x to y such that it is onto and there are exactly three elements in x such that f(x) =b1, is a) 75 b) 90 c) 100 d) 120 Ans: (d) Please explain how t ...

let [x] denote the greatest integer less than (or) equal to x. If f(x)=[x sin (pi*x)] then f(x) is a) cont. at x=0 b) cont. in (-1,0) c) diffn. at x=1 d) diffn in (-1,1) e) none of these ans: a,b,d ...

\lim_{n->infinity}(\sum_{r=1}^{m}{r^{n}})^{1/n} is equal to: (n belongs to Natural nos.) a) m b) m/2 c)em d)em/2 Ans: (a) please tell me the method to solve this..... (SOURCE ARIHANT DIFF CALC.) ...

A ...

\hspace{-16}$Calculate $\mathbf{\int_{0}^{1}x^{2012}.(x^2-1)^5dx}$ ...

∫03 (x2+1)d([x]). [.]→ G.I.F. ...

Let f(x)=x (| x- π|) (2 + cos2x), x∈R. Then the function f: R→R is A) one - one but not onto B) onto but not one one C) both one-one and onto D) neither one one nor onto ...

will anyone explain me the limit of sequence? ...

∫010 [sinxcosx+x2]/[ex+x3-x] ...

Q2 Let f(x) =1+2/x and ffffff.....f(x)=fnx then find the maximum number of real roots of fn(x) a) 0 b) 1 c) 2 d) 3 ...

f(x) is a function satisfying the following condition.... f(x)+f '(x)+f ''(x)+f '''(x) ...upto n terms....= xn where f '(x)=first derivative of x f ''(x)=2nd derivative of x and so on.... Find the value of f(x) + f '(x)/1! + ...

*Image* ...

If 2f(sinx)+f(cosx) = x for all real x, find the domain and range. ...

https://www.youtube.com/watch?v=VX7FptwkkAA ...

\hspace{-16}\mathbf{\int_{0}^{\pi}\frac{25\sin x+2\cos x}{(625\sin^2 x+4\cos^2 x)}dx=} ...

\hspace{-16}$If $\mathbf{A=\int_{0}^{1}\{x^{50}-(2-x)^{50}\}dx}$ and $\mathbf{B=\int_{0}^1\{x^{50}.(1-x)^{50}\}dx}$.\\\\\\ Then $\mathbf{\frac{A}{B}=}$ ...

\hspace{-16}$Let $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ be a Continuous function and $\mathbf{f(x)=f(2x)\forall x\in \mathbb{R}}.$\\\\ If $\mathbf{f(1)=3}$.Then the value of $\mathbf{\int_{-1}^{1}f(f(x))dx=}$ ...

\hspace{-16}$The Curve $\mathbf{y=(\mid x \mid-1)sgn(x-1)}$ Divides $\mathbf{\frac{9x^2}{64}+\frac{4y^2}{25}=\frac{1}{\pi}}$\\\\\\ in Two parts having Area $\mathbf{A_{1}}$ and $\mathbf{A_{2}},$ Where $\mathbf{(A_{1}>A_{2} ...

\hspace{-16}\mathbf{\int_{0}^{5}\left[\{\sin^2 x+\cos(\ln (x))+e^{3x}\}\right]dx=}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function\\\\ and $\mathbf{\{x\}=}$ Fractional part function. ...

\hspace{-16}\mathbf{\int_{1}^{2}\frac{1}{\left(\sqrt{2x-x^2}+2\right)^2}dx} ...

\hspace{-16}$If $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ and $\mathbf{f(x)=\ln(x+\sqrt{x^2+1})}$\\\\ Then no. of solution of the equation $\mathbf{\mid f^{-1}(x)\mid = e^{-\mid x \mid}}$ is ...