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AllQuestion and Answers: Page 587

Question Number 160424 Answers: 1 Comments: 0

Question Number 160420 Answers: 0 Comments: 0

Question Number 160416 Answers: 0 Comments: 5

guys help what does ∐ mean?

$${guys}\:{help} \\ $$$${what}\:{does}\:\coprod\:{mean}? \\ $$

Question Number 160415 Answers: 1 Comments: 0

∫_0 ^∞ (t^n /(1+t+t^2 ))dt=?

$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{t}}^{\boldsymbol{\mathrm{n}}} }{\mathrm{1}+\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\boldsymbol{\mathrm{dt}}=? \\ $$

Question Number 160440 Answers: 0 Comments: 0

lim_(n→∞) ((√(n^2 +n))+nΣ_(k=1) ^n cos ((kπ)/n))=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{n}}+\mathrm{n}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{cos}\:\frac{\mathrm{k}\pi}{\mathrm{n}}\right)=? \\ $$

Question Number 160439 Answers: 0 Comments: 0

lim_(n→∞) ((1/(3π))∫_π ^(2π) (x/(arctan (nx)))dx)^n =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{3}\pi}\int_{\pi} ^{\mathrm{2}\pi} \frac{\mathrm{x}}{\mathrm{arctan}\:\left(\mathrm{nx}\right)}\mathrm{dx}\right)^{\mathrm{n}} =? \\ $$

Question Number 160438 Answers: 0 Comments: 0

lim_(n→∞) (((2(n)^(1/n) −(2)^(1/n) )^n )/n^2 )=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2}\sqrt[{\mathrm{n}}]{\mathrm{n}}−\sqrt[{\mathrm{n}}]{\mathrm{2}}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }=? \\ $$

Question Number 160411 Answers: 1 Comments: 0

Show that tan 58°tan 32° = 1

$$\:\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{tan}\:\mathrm{58}°\mathrm{tan}\:\mathrm{32}°\:=\:\mathrm{1} \\ $$

Question Number 160405 Answers: 1 Comments: 1

1+(1/(1+(2/(1+(1/(1+(2/(1+(1/(....)))))))))) ⇒ x^2 = ?

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}+\frac{\mathrm{1}}{....}}}}}\:\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{2}} \:=\:? \\ $$

Question Number 160409 Answers: 0 Comments: 0

Question Number 160408 Answers: 0 Comments: 0

Question Number 160398 Answers: 0 Comments: 0

Find: 𝛀 =∫_( 0) ^( ∞) ((log(x + 1))/(x^3 + 1)) dx

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{log}\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\mathrm{dx} \\ $$

Question Number 160395 Answers: 1 Comments: 0

I_n =∫_0 ^(π/2) ((sin^2 (nt))/(sin t))dt Find:: lim_(n→∞) (2I_n −lnn)=?

$$\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{nt}\right)}{\mathrm{sin}\:\mathrm{t}}\mathrm{dt} \\ $$$$\mathrm{Find}::\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2I}_{\mathrm{n}} −\mathrm{lnn}\right)=? \\ $$

Question Number 160394 Answers: 0 Comments: 0

lim_(n→∞) ((2/(2^2 −1)))^(1/2^(n−1) ) ((2^2 /(2^3 −1)))^2^(1/(n−2)) ∙...∙((2^(n−1) /(2^n −1)))^(1/2) =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{2}}{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}\right)^{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }} \left(\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{3}} −\mathrm{1}}\right)^{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{n}−\mathrm{2}}} } \centerdot...\centerdot\left(\frac{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }{\mathrm{2}^{\mathrm{n}} −\mathrm{1}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =? \\ $$

Question Number 160391 Answers: 1 Comments: 0

Question Number 160389 Answers: 0 Comments: 2

Question Number 160384 Answers: 2 Comments: 0

lim_(n→∞) n∫_1 ^(1+(1/n)) (√(1+x^n ))dx=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\int_{\mathrm{1}} ^{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}} \sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }\mathrm{dx}=? \\ $$

Question Number 160375 Answers: 1 Comments: 2

Question Number 160373 Answers: 2 Comments: 0

Compare it: ((1 - sin (10°))/(cos (10°))) and 1

$$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\frac{\mathrm{1}\:-\:\mathrm{sin}\:\left(\mathrm{10}°\right)}{\mathrm{cos}\:\left(\mathrm{10}°\right)}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{1} \\ $$

Question Number 160372 Answers: 1 Comments: 0

Calculate Σ_(k=0) ^(2000) i^k , Σ_(k=0) ^(2002) (−1)^k

$${Calculate} \\ $$$$\sum_{{k}=\mathrm{0}} ^{\mathrm{2000}} {i}^{{k}} ,\:\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2002}} \left(−\mathrm{1}\right)^{{k}} \\ $$

Question Number 160371 Answers: 2 Comments: 0

lim_(t→a) (((alnt−tlna)^2 (tlnt−alna))/(2(t−a)(t−a−aln(t/a)))) please help me.

$${li}\underset{{t}\rightarrow{a}} {{m}}\frac{\left({alnt}−{tlna}\right)^{\mathrm{2}} \left({tlnt}−{alna}\right)}{\mathrm{2}\left({t}−{a}\right)\left({t}−{a}−{aln}\frac{{t}}{{a}}\right)} \\ $$$${please}\:{help}\:{me}. \\ $$

Question Number 160363 Answers: 0 Comments: 0

s>0 limΣ_(k=1) ^(2n) ( −1)^( k) .((( k)/(2n)) )^( s) = ?

$$ \\ $$$$\:\:\:\:\:{s}>\mathrm{0} \\ $$$$\:\:\:\:{lim}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\left(\:−\mathrm{1}\right)^{\:{k}} .\left(\frac{\:{k}}{\mathrm{2}{n}}\:\right)^{\:{s}} =\:\:? \\ $$

Question Number 160362 Answers: 0 Comments: 0

∫(x^n /( (√(x−x^2 ))))dx=?

$$\int\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} }{\:\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 160361 Answers: 0 Comments: 0

1^o Prove by recrrence that , for n≥28 , n!≥11^n . 2^o Deduce the limite of the suite (((n!)/(10^n ))) when n tend verse +∞.

$$\mathrm{1}^{{o}} \:{Prove}\:{by}\:{recrrence}\:{that}\:,\:{for} \\ $$$${n}\geqslant\mathrm{28}\:,\:\:{n}!\geqslant\mathrm{11}^{{n}} . \\ $$$$\mathrm{2}^{{o}} \:{Deduce}\:{the}\:{limite}\:{of}\:{the}\:{suite} \\ $$$$\left(\frac{{n}!}{\mathrm{10}^{{n}} }\right)\:{when}\:{n}\:{tend}\:{verse}\:+\infty. \\ $$

Question Number 160358 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(sinx)ln(cosx)dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{sin}{x}\right)\mathrm{ln}\left(\mathrm{cos}{x}\right){dx} \\ $$

Question Number 160353 Answers: 1 Comments: 0

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