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AllQuestion and Answers: Page 25

Question Number 222798    Answers: 1   Comments: 0

Question Number 222787    Answers: 1   Comments: 0

∫_1 ^( π/2) ((4^(−x) ∙ e^(tan(x+x^2 )) ∙ ln(1 + x^3 ))/(1 + x)) dx

$$ \\ $$$$\:\:\:\:\:\int_{\mathrm{1}} ^{\:\pi/\mathrm{2}} \:\:\frac{\mathrm{4}^{−{x}} \:\centerdot\:{e}^{\mathrm{tan}\left({x}+{x}^{\mathrm{2}} \right)} \centerdot\:\mathrm{ln}\left(\mathrm{1}\:+\:{x}^{\mathrm{3}} \right)}{\mathrm{1}\:+\:{x}}\:\:\mathrm{d}{x}\:\:\:\:\: \\ $$$$ \\ $$

Question Number 222783    Answers: 1   Comments: 0

(1/5)x^5 −(5/3)x^3 +4x+2

$$ \\ $$$$ \frac{\mathrm{1}}{\mathrm{5}}{x}^{\mathrm{5}} −\frac{\mathrm{5}}{\mathrm{3}}{x}^{\mathrm{3}} +\mathrm{4}{x}+\mathrm{2} \\ $$$$ \\ $$

Question Number 222781    Answers: 1   Comments: 0

a x^3 +ax^2 +3ax+2

$$ \\ $$$$ \:{a}\: {x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +\mathrm{3}{ax}+\mathrm{2} \\ $$

Question Number 222779    Answers: 1   Comments: 0

Question Number 222778    Answers: 1   Comments: 0

lim_(x→0) ((2log(1+x)−((x(3x+2))/((x+1)^2 )))/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2log}\left(\mathrm{1}+\mathrm{x}\right)−\frac{\mathrm{x}\left(\mathrm{3x}+\mathrm{2}\right)}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 222777    Answers: 1   Comments: 0

Simplify: (((cos214° + i sin146°)∙(cos10° + i sin10°))/((cos66° − i sin246°))) = ?

$$\mathrm{Simplify}: \\ $$$$\frac{\left(\mathrm{cos214}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin146}°\right)\centerdot\left(\mathrm{cos10}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin10}°\right)}{\left(\mathrm{cos66}°\:−\:\boldsymbol{\mathrm{i}}\:\mathrm{sin246}°\right)}\:=\:? \\ $$

Question Number 222760    Answers: 1   Comments: 0

Question Number 222758    Answers: 1   Comments: 1

Question Number 222756    Answers: 1   Comments: 0

lim_(x→0) ((1−(√(cos(x))))/( x−xcos((√x))))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}}{\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{xcos}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)} \\ $$

Question Number 222754    Answers: 1   Comments: 1

Question Number 222753    Answers: 3   Comments: 0

Question Number 222747    Answers: 1   Comments: 1

Question Number 222744    Answers: 0   Comments: 0

Question Number 222743    Answers: 1   Comments: 0

Compare: a = arcctg (√2) b = arccos ((√2)/2) c = arctg (√2)

$$\mathrm{Compare}: \\ $$$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{arcctg}\:\sqrt{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{b}}\:=\:\mathrm{arccos}\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{c}}\:=\:\mathrm{arctg}\:\sqrt{\mathrm{2}} \\ $$

Question Number 222733    Answers: 0   Comments: 0

Question Number 222730    Answers: 2   Comments: 1

Question Number 222736    Answers: 1   Comments: 0

Question Number 222718    Answers: 2   Comments: 3

Question Number 222711    Answers: 1   Comments: 0

Question Number 222705    Answers: 2   Comments: 0

∫_0 ^1 ((lnxarctanx)/x)dx

$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}{x}\mathrm{arctan}{x}}{{x}}{dx} \\ $$

Question Number 222703    Answers: 1   Comments: 1

Question Number 222697    Answers: 1   Comments: 0

Question Number 222685    Answers: 2   Comments: 0

Question Number 222684    Answers: 1   Comments: 1

Question Number 222679    Answers: 2   Comments: 0

If x=Π_(x=1) ^(10) x then (1/(log _2 x))+(1/(log _3 x))+(1/(log _4 x))...+(1/(log _(10) x))=??

$${If}\:{x}=\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}{x}\:{then}\:\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} {x}}...+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} {x}}=?? \\ $$

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