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Question Number 83739 Answers: 0 Comments: 3

what is minimum value of f(x) = (sin x+ csc x )^2 +sec x + cos x

$$\mathrm{what}\:\mathrm{is}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{sin}\:\mathrm{x}+\:\mathrm{csc}\:\mathrm{x}\:\right)^{\mathrm{2}} +\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x} \\ $$

Question Number 83737 Answers: 0 Comments: 0

∫ (x^3 /(x^4 +cos x)) dx ?

$$\int\:\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{4}} +\mathrm{cos}\:{x}}\:{dx}\:? \\ $$

Question Number 83721 Answers: 3 Comments: 8

Question Number 83719 Answers: 2 Comments: 1

Question. ^(Show that ∫_0 ^(Π/2) ((cosx)/(3+cos^2 x))dx=(1/4)ln3)

$${Question}.\:\:\:\:\:\:\:\:\overset{{Show}\:\:{that}\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \frac{{cosx}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx}=\frac{\mathrm{1}}{\mathrm{4}}{ln}\mathrm{3}} {\:} \\ $$

Question Number 83717 Answers: 0 Comments: 0

Question Number 83713 Answers: 1 Comments: 8

∫(dx/(√(x+(√(x+(√x)))))) pleas sir help me

$$\int\frac{{dx}}{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 83710 Answers: 0 Comments: 1

lim_(x→∞) (((1+(√5))^x −(1−(√5))^x )/((1+(√5))^(x−1) −(1−(√5))^(x−1) )) = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} }\:=\:? \\ $$

Question Number 83706 Answers: 1 Comments: 0

4^x + 10^x = 25^x x = ?

$$\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{10}^{\mathrm{x}} \:=\:\mathrm{25}^{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 83694 Answers: 2 Comments: 2

Question Number 83691 Answers: 1 Comments: 2

evaluate: ∫ (( dx)/(a sin x+b cos x))

$$\:\mathrm{evaluate}: \\ $$$$\:\:\:\int\:\frac{\:\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}} \\ $$

Question Number 83690 Answers: 1 Comments: 1

lim_(x→∞ ) ((tan (((πx+1)/(2x+2))))/(x+1)) = ?

$$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\pi{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{2}}\right)}{{x}+\mathrm{1}}\:=\:? \\ $$

Question Number 83680 Answers: 0 Comments: 4

Question Number 83675 Answers: 1 Comments: 2

evaluate: 2 ∫_0 ^( 2) ((√(x+1))/(x^2 +4))dx

$$ \\ $$$$\: \\ $$$$\:\:\mathrm{evaluate}: \\ $$$$\:\mathrm{2}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$$$\:\:\:\:\: \\ $$$$\:\: \\ $$

Question Number 83674 Answers: 1 Comments: 1

Question Number 83672 Answers: 2 Comments: 0

x^2 + (1/x^2 ) = 51 find x

$${x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{51}\: \\ $$$${find}\:{x}\: \\ $$

Question Number 83668 Answers: 1 Comments: 0

lim_(x→0) ((sin x cos x−x)/(x^2 sin (2x))) =

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\: \\ $$

Question Number 83662 Answers: 1 Comments: 3

if f(x) = (√(x^2 −1)) and g(x) = (1/(√(x^2 −3))) find domain function (g • f)(x)

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}} \\ $$$$\mathrm{find}\:\mathrm{domain}\:\mathrm{function}\: \\ $$$$\left(\mathrm{g}\:\bullet\:\mathrm{f}\right)\left(\mathrm{x}\right) \\ $$

Question Number 83654 Answers: 2 Comments: 1

solve this equation sin^2 x−sin^4 x=cos^2 x−cos^4 x

$$\mathrm{solve}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{4}} {x}=\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x} \\ $$

Question Number 83653 Answers: 2 Comments: 0

find range of function y= (4/((x^2 −4)))

$$\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{y}=\:\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)} \\ $$

Question Number 83649 Answers: 1 Comments: 0

Question Number 83644 Answers: 0 Comments: 0

Question Number 83642 Answers: 0 Comments: 0

Find the surface area of the solid generated by the revolution of the cardioids r=a(1+cos θ) about the initial line.

$$ \\ $$$$\: \\ $$$$\mathfrak{Find}\:\mathfrak{the}\:\mathfrak{surface}\:\mathfrak{area}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{solid}\:\mathfrak{generated} \\ $$$$\:\:\mathfrak{by}\:\mathfrak{the}\:\mathfrak{revolution}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{cardioids}\:\mathfrak{r}=\mathfrak{a}\left(\mathrm{1}+\mathfrak{cos}\:\theta\right)\:\mathfrak{about}\:\mathfrak{the}\:\mathfrak{initial}\:\mathfrak{line}. \\ $$

Question Number 83637 Answers: 0 Comments: 0

Question Number 83639 Answers: 4 Comments: 0

Find the differential equations: (i) log((dy/dx))=ax+by (ii) x cos y dy=(x e^x log x +e^x )dx

$$ \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\mathrm{log}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{ax}+\mathrm{by} \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\mathrm{x}\:\mathrm{cos}\:\mathrm{y}\:\mathrm{dy}=\left(\mathrm{x}\:\mathrm{e}^{\mathrm{x}} \mathrm{log}\:\mathrm{x}\:+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 83638 Answers: 1 Comments: 0

Question Number 83629 Answers: 1 Comments: 0

show that Σ_(n,k=0) ^∞ ((n! k!)/((n+k+2)!))=(π^2 /6)

$${show}\:{that} \\ $$$$\underset{{n},{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}!\:{k}!}{\left({n}+{k}+\mathrm{2}\right)!}=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

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