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AllQuestion and Answers: Page 1153

Question Number 90030    Answers: 0   Comments: 0

Question Number 90024    Answers: 0   Comments: 2

sinh^(−1) [ln(x + (√(x^2 + 1)) )] = ?

$$\mathrm{sinh}^{−\mathrm{1}} \left[\mathrm{ln}\left({x}\:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right)\right]\:=\:? \\ $$

Question Number 90023    Answers: 1   Comments: 0

∫ e^(∣x∣) dx = ???

$$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$

Question Number 90019    Answers: 1   Comments: 0

find the gcd(2467, 1367)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{gcd}\left(\mathrm{2467},\:\mathrm{1367}\right) \\ $$

Question Number 90018    Answers: 1   Comments: 2

expand , ln(1 + sin x) right up to the term in x^3

$$\mathrm{expand}\:,\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{sin}\:{x}\right)\:\mathrm{right}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{3}} \\ $$

Question Number 90013    Answers: 1   Comments: 2

−p^2 +2027=−q^2 p+q=?

$$−{p}^{\mathrm{2}} +\mathrm{2027}=−{q}^{\mathrm{2}} \\ $$$${p}+{q}=? \\ $$

Question Number 90011    Answers: 0   Comments: 6

Question Number 90009    Answers: 0   Comments: 0

Σ_(n=0) ^∞ ((((√2)−1)^(2n+1) )/((2n+1)^2 ))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$

Question Number 90003    Answers: 0   Comments: 0

show that ∫_(−∞) ^∞ (dx/(1+(x+tan(x))^(2 ) ))=π

$${show}\:{that} \\ $$$$\int_{−\infty} ^{\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tan}\left({x}\right)\right)^{\mathrm{2}\:} }=\pi \\ $$

Question Number 89994    Answers: 2   Comments: 0

x−y=3(√(xy)) ((x/y)−1)^3 +((y/x)−1)^3 = ?

$$\mathrm{x}−\mathrm{y}=\mathrm{3}\sqrt{\mathrm{xy}} \\ $$$$\left(\frac{\mathrm{x}}{\mathrm{y}}−\mathrm{1}\right)^{\mathrm{3}} +\left(\frac{\mathrm{y}}{\mathrm{x}}−\mathrm{1}\right)^{\mathrm{3}} \:=\:? \\ $$

Question Number 89991    Answers: 0   Comments: 2

if a,b > 0 and (a^2 /b^2 ) = (5/3) find ((a^2 +b^2 )/(ab))

$$\mathrm{if}\:\mathrm{a},\mathrm{b}\:>\:\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{ab}} \\ $$

Question Number 89986    Answers: 0   Comments: 3

∫_0 ^1 (−1)^(⌊(1/x)⌋) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \:{dx} \\ $$

Question Number 89980    Answers: 0   Comments: 2

Question Number 89978    Answers: 0   Comments: 1

(x (dy/dx)−y)(cos (((2y)/x))) = −3x^4

$$\left(\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{2y}}{\mathrm{x}}\right)\right)\:=\:−\mathrm{3x}^{\mathrm{4}} \\ $$

Question Number 89977    Answers: 0   Comments: 2

Question Number 89973    Answers: 1   Comments: 1

x (dy/dx) −y = x^2 tan ((y/x))

$${x}\:\frac{{dy}}{{dx}}\:−{y}\:=\:{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)\: \\ $$

Question Number 89970    Answers: 0   Comments: 1

xy (dy/dx) = y^2 ((x^3 /(x^2 +1)))

$$\mathrm{xy}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$

Question Number 89955    Answers: 1   Comments: 2

9^(x+1) ∤28(3^x )+3=0

$$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$

Question Number 89953    Answers: 0   Comments: 1

solvethefollowingequation 5^(2x+y) =625and2^(4x∤2y) =(1/6)

$$\mathrm{solvethefollowingequation} \\ $$$$\mathrm{5}^{\mathrm{2x}+\mathrm{y}} =\mathrm{625and2}^{\mathrm{4x}\nmid\mathrm{2y}} =\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 89951    Answers: 0   Comments: 1

log _2 (sin (x+((5π)/(12)))) + log _2 (sin (x+(π/(12))))=−1

$$\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{sin}\:\left({x}+\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\right)\:+\:\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{12}}\right)\right)=−\mathrm{1} \\ $$

Question Number 89950    Answers: 0   Comments: 1

Question Number 89946    Answers: 1   Comments: 0

∫ _(−(π/2)) ^(π/2) (dx/(1+e^(sin x) ))

$$\int\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} } \\ $$

Question Number 89958    Answers: 0   Comments: 1

prove that (1+sin x/1+cos 3(1sin x/1+cosec x)=tanx

$${prove}\:{that}\:\left(\mathrm{1}+\mathrm{sin}\:{x}/\mathrm{1}+\mathrm{cos}\:\mathrm{3}\left(\mathrm{1sin}\:{x}/\mathrm{1}+\mathrm{cosec}\:{x}\right)={tanx}\right. \\ $$

Question Number 89956    Answers: 0   Comments: 1

simplifyκgivingκyourκanswerκinκindexκform (√((ac^2 )/(9a^2 c^4 )))

$$\mathrm{simplify}\kappa\mathrm{giving}\kappa\mathrm{your}\kappa\mathrm{answer}\kappa\mathrm{in}\kappa\mathrm{index}\kappa\mathrm{form} \\ $$$$\sqrt{\frac{\mathrm{ac}^{\mathrm{2}} }{\mathrm{9a}^{\mathrm{2}} \mathrm{c}^{\mathrm{4}} }} \\ $$

Question Number 89938    Answers: 0   Comments: 1

If x(x+1) = 1 find (x+1)^3 −(1/((x+1)^3 ))

$$\mathrm{If}\:\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{find}\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} −\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 89937    Answers: 0   Comments: 1

Prove that for all complex such as ∣z∣<1= Σ_(n=1) ^∞ (z^n /((z^n −1)^2 )) +Σ_(n=1) ^∞ ((nz^n )/(z^n −1)) = 0

$${Prove}\:{that}\:{for}\:{all}\:{complex}\:{such}\:{as}\:\mid{z}\mid<\mathrm{1}= \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{z}^{{n}} }{\left({z}^{{n}} −\mathrm{1}\right)^{\mathrm{2}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{nz}^{{n}} }{{z}^{{n}} −\mathrm{1}}\:=\:\mathrm{0}\: \\ $$

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