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Question Number 201545 Answers: 0 Comments: 0

Question Number 201544 Answers: 2 Comments: 0

Question Number 201533 Answers: 2 Comments: 0

Un = ln (cos (1/2^n ) ) show that Un ≤0

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:{ln}\:\left({cos}\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\right) \\ $$$$\:\:\:\:{show}\:\:{that}\:{Un}\:\leqslant\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201534 Answers: 0 Comments: 1

let f(x)=tanx find f^((n)) (x) with n integr natural

$${let}\:{f}\left({x}\right)={tanx} \\ $$$${find}\:{f}^{\left({n}\right)} \left({x}\right)\:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$

Question Number 201527 Answers: 1 Comments: 0

Question Number 201526 Answers: 1 Comments: 0

Question Number 201519 Answers: 3 Comments: 0

Question Number 201517 Answers: 1 Comments: 0

Question Number 201516 Answers: 1 Comments: 0

Question Number 201515 Answers: 1 Comments: 0

Question Number 201555 Answers: 1 Comments: 0

Question Number 201557 Answers: 2 Comments: 0

5 ∙ 555...5_( 50) find the sum of the digits of the product.

$$\mathrm{5}\:\centerdot\:\underset{\:\mathrm{50}} {\underbrace{\mathrm{555}...\mathrm{5}}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{product}. \\ $$

Question Number 201510 Answers: 1 Comments: 0

Question Number 201509 Answers: 1 Comments: 0

Question Number 201502 Answers: 0 Comments: 3

A generation is about one-third of a lifetime.Approximately about how many generations have passed since the year 0AD?

$${A}\:{generation}\:{is}\:{about}\:{one}-{third}\:{of}\:{a} \\ $$$${lifetime}.{Approximately}\:{about}\:{how} \\ $$$${many}\:{generations}\:{have}\:{passed}\:{since} \\ $$$${the}\:{year}\:\mathrm{0}{AD}? \\ $$

Question Number 201514 Answers: 0 Comments: 0

Question Number 201495 Answers: 1 Comments: 1

(Un)_(n≥1 ;) (1/(nC_(2n) ^n )) study convergence

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\left({Un}\right)_{{n}\geqslant\mathrm{1}\:;} \:\:\:\:\frac{\mathrm{1}}{{nC}_{\mathrm{2}{n}} ^{{n}} \:} \\ $$$$ \\ $$$$\:\:\:\:{study}\:\:{convergence} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201486 Answers: 0 Comments: 0

Question Number 201477 Answers: 1 Comments: 0

how to prove that (3d_3 +4d_2 +3d_1 )^2 ≤5(d_1 ^2 +d_2 ^2 +d_3 ^2 +(d_2 +d_1 )^2 +(d_3 +d_2 )^2 +(d_1 +d_2 +d_3 )^2 )

$$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\left(\mathrm{3d}_{\mathrm{3}} +\mathrm{4d}_{\mathrm{2}} +\mathrm{3d}_{\mathrm{1}} \right)^{\mathrm{2}} \leqslant\mathrm{5}\left(\mathrm{d}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{d}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{d}_{\mathrm{3}} ^{\mathrm{2}} +\left(\mathrm{d}_{\mathrm{2}} +\mathrm{d}_{\mathrm{1}} \right)^{\mathrm{2}} +\left(\mathrm{d}_{\mathrm{3}} +\mathrm{d}_{\mathrm{2}} \right)^{\mathrm{2}} +\left(\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} +\mathrm{d}_{\mathrm{3}} \right)^{\mathrm{2}} \right) \\ $$

Question Number 201475 Answers: 0 Comments: 5

Question Number 201473 Answers: 0 Comments: 0

∫_0 ^1 ((Li_3 (−x^2 ))/(1+x))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{Li}}_{\mathrm{3}} \left(−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 201464 Answers: 2 Comments: 0

if f(2) = 3 and f(4) = 5 find ∫_2 ^( 4) f(x) ∙ f^′ (x) dx = ?

$$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:\mathrm{3}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{4}\right)\:=\:\mathrm{5} \\ $$$$\mathrm{find}\:\:\:\int_{\mathrm{2}} ^{\:\mathrm{4}} \:\mathrm{f}\left(\mathrm{x}\right)\:\centerdot\:\mathrm{f}\:^{'} \left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 201452 Answers: 2 Comments: 0

Question Number 201447 Answers: 0 Comments: 0

Question Number 201445 Answers: 0 Comments: 0

Question Number 201443 Answers: 1 Comments: 5

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