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Question Number 83781 Answers: 1 Comments: 2

∫ _0^(π/2) (1/(4sin^2 x+5cos^2 x)) dx

$$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 83774 Answers: 1 Comments: 0

Given 2(√(log_3 x−1)) − log_3 x^3 +8 > 0 have the solution a ≤ x < b. what is b ?

$$\mathrm{Given}\:\mathrm{2}\sqrt{\mathrm{log}_{\mathrm{3}} \:{x}−\mathrm{1}}\:−\:\mathrm{log}_{\mathrm{3}} \:{x}^{\mathrm{3}} \:+\mathrm{8}\:>\:\mathrm{0} \\ $$$${have}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{a}\:\leqslant\:{x}\:<\:{b}.\: \\ $$$${what}\:{is}\:{b}\:?\: \\ $$

Question Number 83767 Answers: 2 Comments: 1

Question Number 83759 Answers: 2 Comments: 3

3^x 8^(x/(x+2)) =6

$$\mathrm{3}^{{x}} \:\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6} \\ $$

Question Number 83756 Answers: 0 Comments: 3

Find all real solutions of (x, y) such that x + 3y + (4/(x + y)) = 5 y + 3x + (5/(x + y)) = 7

$${Find}\:\:{all}\:\:{real}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\mathrm{3}{y}\:+\:\frac{\mathrm{4}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:{y}\:+\:\mathrm{3}{x}\:+\:\frac{\mathrm{5}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{7} \\ $$

Question Number 83750 Answers: 0 Comments: 0

I=∫e^x tan(x) dx

$${I}=\int{e}^{{x}} \:{tan}\left({x}\right)\:{dx} \\ $$

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

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