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Question Number 144699 Answers: 3 Comments: 0

let f(x)=log(cht) developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{cht}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 144697 Answers: 2 Comments: 0

Evaluate (((1+cos (π/(10))−isin (π/(10)))/(1+cos (π/(10))+isin (π/(10)))))^(15) .

$$\mathrm{Evaluate}\:\left(\frac{\mathrm{1}+\mathrm{cos}\:\frac{\pi}{\mathrm{10}}−{i}\mathrm{sin}\:\frac{\pi}{\mathrm{10}}}{\mathrm{1}+\mathrm{cos}\:\frac{\pi}{\mathrm{10}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{10}}}\right)^{\mathrm{15}} . \\ $$

Question Number 144693 Answers: 1 Comments: 0

Question Number 144691 Answers: 1 Comments: 0

Question Number 144684 Answers: 1 Comments: 0

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Question Number 144683 Answers: 1 Comments: 0

Determiner l′original de laplace F(p)=(1/((p^2 +p+1)^2 ))

$${Determiner}\:{l}'{original}\:{de}\:{laplace} \\ $$$${F}\left({p}\right)=\frac{\mathrm{1}}{\left({p}^{\mathrm{2}} +{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 144682 Answers: 1 Comments: 0

Compare: x=((sin(3))/(sin(5))) and y=((cos(3))/(cos(5)))

$${Compare}:\:\:{x}=\frac{{sin}\left(\mathrm{3}\right)}{{sin}\left(\mathrm{5}\right)}\:\:{and}\:\:{y}=\frac{{cos}\left(\mathrm{3}\right)}{{cos}\left(\mathrm{5}\right)} \\ $$

Question Number 144663 Answers: 1 Comments: 0

x∈(0;π) and (a;b) real numbers fixed. Find the range of function: g(x)= (((1+a^2 +cot^2 x)∙(1+b^2 +cot^2 x))/(1 + cot^2 x))

$${x}\in\left(\mathrm{0};\pi\right)\:{and}\:\left({a};{b}\right)\:{real}\:{numbers}\:{fixed}. \\ $$$${Find}\:{the}\:{range}\:{of}\:{function}: \\ $$$${g}\left({x}\right)=\:\frac{\left(\mathrm{1}+{a}^{\mathrm{2}} +{cot}^{\mathrm{2}} {x}\right)\centerdot\left(\mathrm{1}+{b}^{\mathrm{2}} +{cot}^{\mathrm{2}} {x}\right)}{\mathrm{1}\:+\:{cot}^{\mathrm{2}} {x}} \\ $$

Question Number 144662 Answers: 1 Comments: 0

........... Calculus........... In AB^Δ C : B^ = 2 C^ , a = λ b then specify the limits of the changes ′ λ ′ :

$$\:\:\:\:\:\:\:...........\:\:\mathrm{Calculus}........... \\ $$$$\:\mathrm{In}\:\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\:: \\ $$$$\hat {\mathrm{B}}\:=\:\mathrm{2}\:\hat {\mathrm{C}}\:\:\:\:,\:\:{a}\:\:=\:\lambda\:{b}\:\:\:{then}\:{specify} \\ $$$$\:{the}\:\:{limits}\:{of}\:{the}\:{changes}\:\:\:'\:\:\lambda\:\:'\:\:: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 144676 Answers: 1 Comments: 0

Let a,b,c > 0 and (a+b)(b+c) = 4. Prove that (1/a)+(1/b)+(1/c)+(b/(ca)) ≥ ((27)/8) (Found by WolframAlpha)

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{4}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}+\frac{{b}}{{ca}}\:\geqslant\:\frac{\mathrm{27}}{\mathrm{8}} \\ $$$$\left(\mathrm{Found}\:\mathrm{by}\:\mathrm{WolframAlpha}\right) \\ $$

Question Number 144645 Answers: 2 Comments: 0

lim_(x→0) (((1 + tanx)/(1 + sinx)))^(1/(sinx)) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\mathrm{1}\:+\:{tanx}}{\mathrm{1}\:+\:{sinx}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{sinx}}}} =\:? \\ $$

Question Number 144639 Answers: 0 Comments: 0

Question Number 144638 Answers: 1 Comments: 0

Triangle AOC inscribed in the region cut from the parabola y=x^2 by the line y=a^2 .Find the limit of ratio of the area of the triangle to the area of the parabolic region as a approaches zero

$$\mathrm{Triangle}\:\mathrm{AOC}\:\mathrm{inscribed} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mathrm{cut}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{line}\:\mathrm{y}=\mathrm{a}^{\mathrm{2}} \:.\mathrm{Find}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\mathrm{of}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangle}\:\mathrm{to}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{parabolic}\:\mathrm{region}\:\mathrm{as}\:\mathrm{a}\:\mathrm{approaches} \\ $$$$\mathrm{zero}\: \\ $$

Question Number 144636 Answers: 1 Comments: 0

Find the areas of the regions enclosed by the lines and curves x=y^2 −1 and x=∣y∣(√(1−y^2 ))

$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{regions} \\ $$$$\:\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{and}\:\mathrm{curves} \\ $$$$\:\:\:\mathrm{x}=\mathrm{y}^{\mathrm{2}} −\mathrm{1}\:\mathrm{and}\:\mathrm{x}=\mid\mathrm{y}\mid\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\: \\ $$$$ \\ $$

Question Number 144634 Answers: 2 Comments: 0

Let a,b,c > 0 and (a+b)(b+c) = 4. Prove that (1) a^2 +2b^2 +c^2 +((2b(c^2 +a^2 ))/(c+a)) ≥ 6 (2) a^3 +3b^3 +c^3 +((3b(c^3 +a^3 ))/(c+a)) ≥ 8 (3) a^4 +4b^4 +c^4 +((4b(c^4 +a^4 ))/(c+a)) ≥ 10

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{4}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{2}} +\mathrm{2}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\frac{\mathrm{2}{b}\left({c}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{{c}+{a}}\:\geqslant\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{3}} +\mathrm{3}{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +\frac{\mathrm{3}{b}\left({c}^{\mathrm{3}} +{a}^{\mathrm{3}} \right)}{{c}+{a}}\:\geqslant\:\mathrm{8} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{4}} +\mathrm{4}{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +\frac{\mathrm{4}{b}\left({c}^{\mathrm{4}} +{a}^{\mathrm{4}} \right)}{{c}+{a}}\:\geqslant\:\mathrm{10} \\ $$

Question Number 144629 Answers: 1 Comments: 0

if f^2 (2x-1)-10f(3x-2)+25=0 find f^′ (1)+f(1)=?

$${if}\:\:{f}^{\mathrm{2}} \left(\mathrm{2}{x}-\mathrm{1}\right)-\mathrm{10}{f}\left(\mathrm{3}{x}-\mathrm{2}\right)+\mathrm{25}=\mathrm{0} \\ $$$${find}\:\:{f}\:^{'} \left(\mathrm{1}\right)+{f}\left(\mathrm{1}\right)=? \\ $$

Question Number 144622 Answers: 2 Comments: 0