Recently Active Calculus Questions

f(x)= xn sinx cosx n! sin((npi)/2) cos((npi)/2) a a2 a3 show that dn/dxn[f(x)] at x=0 is 0.... ...

\mathbf{\int_{0}^{1}\frac{1}{(1+x^{2011}).\sqrt[2011]{(1+x^{2011})}}dx}$ ...

how to integrate cosec ^3 x w.r.t x? ...

Q. Evaluate: \lim_{n\rightarrow \infty}\frac{[1^{2}x]+[2^{2}x]+[3^{2}x]+ ...+[n^{2}x]}{n^{3}} , [.] \; is \; G.I.F ...

$\textbf{Find Max. and Min. value of the expression}\\\\ $\mathbf{f(x)=\sum_{k=0}^{27}\left\{^{27}C_{k}.\left(\frac{x}{100}\right)^k}.\left(\frac{100-x}{100}\right)^{27-k}.\left(80k-23x\right)\right\}$.\textbf{Where} $\mathbf ...

Consider an arbitrary function f:X→Y. It includes two important set mappings. If A is a subset of X, then its image f(A) is the subset of Y defined by f(A)={f(x) : x ε A}. Similarly, if B is a subset of Y, then its inverse ...

i thought my mouse was not working and clicked on "Add post" several times !!! Extremely sorry....!!! how to delete a post ????? ...

1. Let f(x)=\frac{x+1}{2x-1} and g(x)=\left|x \right| + 1 . Then the number of elements in the set \left\{{x:f(x)\geq g(x)} \right\}\sim \left[\left\left(1/2,3/5 \right)\cup\left(3/5,7/10 \right)\cup\left(7/10,4/5 \right)\cup ...

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Q. If α =e 2π/11 and f(x)=5+\sum_{k=1}^{60}{A_{k}x^{k}} , then find the value of \frac{1}{11}\sum_{r=0}^{10}{f(\alpha ^{r}x}) . Note: Integer type! ...

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\mathbf{\int_{-1}^{1}\frac{dx}{1+x+x^2+\sqrt{x^4+3x^2+1}}}$\\\\ Ans::\Leftrightarrow $\mathbf{=\frac{\pi}{4}}$ ...

$Q$:$\Rightarrow$ $Find Min. value of $\int_{0}^{\frac{4\pi}{3}}|sinx-c|dx$, Where $c\geq0.$ ...

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Q. IF x= a sec θ, y = b tan θ, prove that d2y/dx2 = - b4/a2y3. ...

Tangents are drawn to curve y=sinx from the origin. Find the locus of points of contact of these tangents. ...

$Calculate $\int_{0}^{\infty}\frac{tan^{-1}(\frac{x}{3})+tan^{-1}(3x)}{1+x^2}dx$ = ...

The equation ∏/2∫x sin2y. dy= 0 has: A) NO SOLUTION B) ONE SOLUTION C) TWO SOLUTIONS D) THREE SOLUTIONS ...

Evaluate : \int_{-1}^{1}{\frac{\ln(13-6\cos{x})dx}{\sqrt{1-x^2}}} ...

find the max value of (cos\,\, \alpha _{1}) (cos\,\, \alpha _{2}) ...... (cos\,\, \alpha _{n}) under the restrictions 0\leq \alpha _{i}\leq \Pi /2 and (cot\,\, \alpha _{1}) (cot\,\, \alpha _{2}) ...... (cot\,\, \alpha _{n}) = ...

If f(x)=\frac{ax}{x+1} , x\neq -1 then for what value of a is f(f(x))=x ? ...

\mathbf{\lim_{n\to\infty}n.\int_{0}^{\frac{\pi}{2}}\left(1-\sqrt[n]{sinx}\right)dx=}$\\\\ \textbf{Ans::\Rightarrow \mathbf{\displaystyle \frac{\pi.ln(2)}{2}}} ...

\mathbf{\lim_{n\to\infty}\left\{\left(\sqrt{3}+1\right)^{2n}\right\}}=$\\\\ \textbf{Where $\mathbf{\left\{.\right\} = }$Fractional part of $\mathbf{x}$} ...

The order and degree of the D.E. (y+c)2=cx is? I got the answer as 2,1 resp. but the answer given is opposite. What do you say? ...

\mathbf{\int_{0}^{1}\frac{dx}{x.(x+1).\left\{ln\left(1+\frac{1}{x}\right)\right\}^{2011}}}=$ ...

\mathbf{\int_{0}^{\pi}|sin(2x)-sin(3x)|dx=}\\\\ \textbf{Ans::}=\frac{5\sqrt{5}+4}{6} ...

\mathbf{\int\frac{dx}{(x+2)^5(x+3)^3}=}$ ...

Solve: (e^4x)*(p-1) + (e^2y)*(p^2) = 0 ...

$If $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ and $\mathbf{\frac{\sqrt{5}+1}{2}f(x)=f(x+1)+f(x-1)\forall x\in \mathbb{R}}$.\\\\ Then find Period of $\mathbf{f(x)}$\\\\ Ans:=$\mathbf{10}$ ...