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Question Number 163428 Answers: 0 Comments: 2

jusgifier la convergence de ∫_0 ^1 ln(1−x^2 )dx

$${jusgifier}\:{la}\:{convergence}\:{de}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 163414 Answers: 1 Comments: 0

∫(dx/( (√(cosx sin^3 x))+(√(sinx cos^3 x))))

$$\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{cosx}}\:\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}+\sqrt{\boldsymbol{{sinx}}\:\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}} \\ $$

Question Number 163413 Answers: 0 Comments: 3

Question Number 163408 Answers: 1 Comments: 0

((1+(2/9)(√(21))))^(1/3) +((1−(2/9)(√(21))))^(1/3) =?

$$\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{9}}\sqrt{\mathrm{21}}}=? \\ $$

Question Number 163402 Answers: 1 Comments: 0

∫_0 ^1 (x−1)^(10) (x−3)^3 dx

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{10}} \left(\boldsymbol{{x}}−\mathrm{3}\right)^{\mathrm{3}} \boldsymbol{{dx}} \\ $$

Question Number 163411 Answers: 0 Comments: 0

Question Number 163400 Answers: 2 Comments: 0

prove Ω= ∫_0 ^( ∞) cot^( −1) (1+x^( 2) )=((√((1/( (√2)))−(1/2))) ) π

$$ \\ $$$$\:\:\:\:\:{prove}\: \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} {cot}^{\:−\mathrm{1}} \left(\mathrm{1}+{x}^{\:\mathrm{2}} \right)=\left(\sqrt{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{1}}{\mathrm{2}}}\:\right)\:\:\pi \\ $$$$ \\ $$

Question Number 163397 Answers: 0 Comments: 5

Question Number 163396 Answers: 0 Comments: 0

if a and b are positive numbers then Σ (an + b)^(-p) converges if p>1 and diverges if p≤1

$$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\mathrm{then}\:\:\Sigma\:\left(\mathrm{an}\:+\:\mathrm{b}\right)^{-\boldsymbol{\mathrm{p}}} \:\:\mathrm{converges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}>\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{diverges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}\leqslant\mathrm{1} \\ $$

Question Number 163393 Answers: 1 Comments: 0

Question Number 163386 Answers: 1 Comments: 0

lim_(x→−∞) ((1−x^3 ))^(1/3) −((x^4 −1))^(1/4)

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }−\sqrt[{\mathrm{4}}]{{x}^{\mathrm{4}} −\mathrm{1}} \\ $$

Question Number 163385 Answers: 1 Comments: 0

Question Number 163384 Answers: 2 Comments: 0

Question Number 163383 Answers: 0 Comments: 0

Question Number 163435 Answers: 1 Comments: 0

Question Number 163378 Answers: 0 Comments: 0

Question Number 163368 Answers: 1 Comments: 0

Question Number 163367 Answers: 2 Comments: 0

Question Number 163357 Answers: 1 Comments: 0

∫_0 ^( 1) ln(3x−3x^( 2) + x^( 3) )= ?

$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\mathrm{3}{x}−\mathrm{3}{x}^{\:\mathrm{2}} +\:{x}^{\:\mathrm{3}} \right)=\:? \\ $$$$ \\ $$

Question Number 163349 Answers: 1 Comments: 0

Question Number 163346 Answers: 0 Comments: 2

how do i calculate for (1/2)!

$${how}\:{do}\:{i}\:{calculate}\:{for}\:\frac{\mathrm{1}}{\mathrm{2}}! \\ $$

Question Number 163340 Answers: 1 Comments: 0

Question Number 163333 Answers: 0 Comments: 2

∫_0 ^(π/2) ((√(sinx))/( (√(sinx))+(√(cosx))))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\sqrt{{sinx}}}{\:\sqrt{{sinx}}+\sqrt{{cosx}}}{dx} \\ $$

Question Number 163327 Answers: 1 Comments: 0

(1+((20)/(100)))^n =((216)/(125)) n=?

$$\left(\mathrm{1}+\frac{\mathrm{20}}{\mathrm{100}}\right)^{{n}} =\frac{\mathrm{216}}{\mathrm{125}}\:\:\:\:\:\:{n}=? \\ $$

Question Number 163325 Answers: 1 Comments: 2

2a=(1/( (√1)+(√2)))+(1/( (√2)+(√3)))+...+(1/( (√(2024))+(√(2025))))=?

$$\mathrm{2}{a}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}+\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+...+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2024}}+\sqrt{\mathrm{2025}}}=? \\ $$

Question Number 163324 Answers: 1 Comments: 0

Given that {a_n } is a geometric sequence where the first term, a_1 >1 and the common ratio, r>0. If b_n =log_2 a_n where n∈N, b_1 +b_3 +b_5 =6, and b_1 ∙b_3 ∙b_5 =0, find the general term of {a_n }.

$$\mathrm{Given}\:\mathrm{that}\:\left\{{a}_{{n}} \right\}\:\mathrm{is}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{sequence} \\ $$$$\mathrm{where}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term},\:{a}_{\mathrm{1}} >\mathrm{1}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{ratio},\:{r}>\mathrm{0}.\: \\ $$$$\mathrm{If}\:{b}_{{n}} =\mathrm{log}_{\mathrm{2}} \:{a}_{{n}} \:\mathrm{where}\:{n}\in\mathbb{N},\:{b}_{\mathrm{1}} +{b}_{\mathrm{3}} +{b}_{\mathrm{5}} =\mathrm{6}, \\ $$$$\mathrm{and}\:{b}_{\mathrm{1}} \centerdot{b}_{\mathrm{3}} \centerdot{b}_{\mathrm{5}} =\mathrm{0},\:\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{term}\:\mathrm{of}\:\left\{{a}_{{n}} \right\}. \\ $$

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