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Question Number 206490    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((cos (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206489    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((sin (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206484    Answers: 1   Comments: 0

Question Number 206477    Answers: 3   Comments: 0

If a>b>0 and 4a^2 + b^2 = 4ab Find: ((a − b)/(a + b)) = ?

$$\mathrm{If}\:\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4ab} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{a}\:−\:\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$

Question Number 206475    Answers: 1   Comments: 0

If (a^2 /(12)) − 5b^3 = −30 Find: (2/(45)) a^2 − (8/3) b^3 = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{12}}\:−\:\mathrm{5b}^{\mathrm{3}} \:=\:−\mathrm{30} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2}}{\mathrm{45}}\:\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{8}}{\mathrm{3}}\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 206473    Answers: 4   Comments: 0

If 4^p = 5 Find: 2^(3p) = ?

$$\mathrm{If}\:\:\:\mathrm{4}^{\boldsymbol{\mathrm{p}}} \:=\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{2}^{\mathrm{3}\boldsymbol{\mathrm{p}}} \:=\:? \\ $$

Question Number 206471    Answers: 1   Comments: 0

If asinθ = bcosθ = ((2ctanθ)/(1 − tan^2 θ)) then prove that (a^2 − b^2 )^2 = 4c^2 (a^2 + b^2 ).

$$\mathrm{If}\:{a}\mathrm{sin}\theta\:=\:{b}\mathrm{cos}\theta\:=\:\frac{\mathrm{2}{c}\mathrm{tan}\theta}{\mathrm{1}\:−\:\mathrm{tan}^{\mathrm{2}} \theta}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\left({a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \right)^{\mathrm{2}} \:=\:\mathrm{4}{c}^{\mathrm{2}} \left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right). \\ $$

Question Number 206466    Answers: 1   Comments: 1

Question Number 206458    Answers: 3   Comments: 0

if f(x)=(√(x−x^2 )) then f^(−1) (x)=?

$${if}\:{f}\left({x}\right)=\sqrt{{x}−{x}^{\mathrm{2}} }\:\:\:\:\:{then}\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 206452    Answers: 1   Comments: 0

Question Number 206451    Answers: 0   Comments: 0

Question Number 206449    Answers: 1   Comments: 0

solve the first order differential equation: xdy − ydx = (xy)^(1/2) dx

$${solve}\:{the}\:{first}\:{order}\:{differential} \\ $$$${equation}: \\ $$$$ \\ $$$${xdy}\:−\:{ydx}\:=\:\left({xy}\right)^{\mathrm{1}/\mathrm{2}} {dx} \\ $$

Question Number 206443    Answers: 0   Comments: 4

Question Number 206442    Answers: 1   Comments: 0

Question Number 206434    Answers: 1   Comments: 0

If tan^2 θ = 1 − x^2 then prove that secθ + tan^3 θcosecθ = (√((2 − x^2 )^3 )) .

$$\mathrm{If}\:\mathrm{tan}^{\mathrm{2}} \theta\:=\:\mathrm{1}\:−\:{x}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{sec}\theta\:+\:\mathrm{tan}^{\mathrm{3}} \theta\mathrm{cosec}\theta\:=\:\sqrt{\left(\mathrm{2}\:−\:{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:. \\ $$

Question Number 206433    Answers: 2   Comments: 0

let f:[0,∞)→R be a continuous function if lim_(n→∞ ) ∫_0 ^1 f(x+n)dx = 2 then lim_(n→∞) f(nx) = ?

$$\:\:\:\:\:\mathrm{let}\:\mathrm{f}:\left[\mathrm{0},\infty\right)\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{if} \\ $$$$\:\:\:\:\underset{\mathrm{n}\rightarrow\infty\:} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}+\mathrm{n}\right)\mathrm{dx}\:=\:\mathrm{2} \\ $$$$\:\mathrm{then}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{nx}\right)\:=\:? \\ $$$$\: \\ $$

Question Number 206430    Answers: 2   Comments: 0

Question Number 206425    Answers: 1   Comments: 0

If cos𝛂 = (3/5) (0<𝛂<(𝛑/2)) Find: ((tan^2 (45° + (𝛂/2)))/3) = ?

$$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\left(\mathrm{0}<\boldsymbol{\alpha}<\frac{\boldsymbol{\pi}}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{45}°\:+\:\frac{\boldsymbol{\alpha}}{\mathrm{2}}\right)}{\mathrm{3}}\:=\:? \\ $$

Question Number 206421    Answers: 1   Comments: 0

If tanpθ = ptanθ then prove that ((sin^2 pθ)/(sin^2 θ)) = (p^2 /(1 + (p^2 − 1)sin^2 θ)) .

$$\mathrm{If}\:\mathrm{tan}{p}\theta\:=\:{p}\mathrm{tan}\theta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} {p}\theta}{\mathrm{sin}^{\mathrm{2}} \theta}\:=\:\frac{{p}^{\mathrm{2}} }{\mathrm{1}\:+\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\mathrm{sin}^{\mathrm{2}} \theta}\:.\: \\ $$

Question Number 206399    Answers: 2   Comments: 1

Question Number 206396    Answers: 3   Comments: 0

Question Number 206394    Answers: 0   Comments: 1

Question Number 206393    Answers: 1   Comments: 0

find S=1+Σ_ℓ (((−)^ℓ )/ℓ)((1/ℓ)−(1/(ℓ+1))) , ℓ∈[1,∞) 1+Σ_ℓ (((−)^ℓ )/ℓ)((1/ℓ)−(1/(ℓ+1))) 1−(1−(1/2))+(1/2)((1/2)−(1/3))−(1/3)((1/3)−(1/4))+(1/4)((1/4)−(1/5))−......

$$\mathrm{find}\:\mathrm{S}=\mathrm{1}+\underset{\ell} {\sum}\:\frac{\left(−\right)^{\ell} }{\ell}\left(\frac{\mathrm{1}}{\ell}−\frac{\mathrm{1}}{\ell+\mathrm{1}}\right)\:,\:\ell\in\left[\mathrm{1},\infty\right) \\ $$$$\mathrm{1}+\underset{\ell} {\sum}\:\frac{\left(−\right)^{\ell} }{\ell}\left(\frac{\mathrm{1}}{\ell}−\frac{\mathrm{1}}{\ell+\mathrm{1}}\right) \\ $$$$\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\right)−\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{5}}\right)−...... \\ $$

Question Number 206391    Answers: 2   Comments: 0

Find: ∫_(−3) ^( −2) (∣x∣ + ∣x − 4∣) dx = ?

$$\mathrm{Find}: \\ $$$$\int_{−\mathrm{3}} ^{\:−\mathrm{2}} \:\left(\mid\mathrm{x}\mid\:+\:\mid\mathrm{x}\:−\:\mathrm{4}\mid\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 206365    Answers: 2   Comments: 4

Number series: a_3 = 2a + b − 6 a_9 = a + b + 5 a_(15) = 3a + b − 7 Find: a = ?

$$\mathrm{Number}\:\mathrm{series}: \\ $$$$\mathrm{a}_{\mathrm{3}} \:=\:\mathrm{2a}\:+\:\mathrm{b}\:−\:\mathrm{6} \\ $$$$\mathrm{a}_{\mathrm{9}} \:=\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{5} \\ $$$$\mathrm{a}_{\mathrm{15}} \:=\:\mathrm{3a}\:+\:\mathrm{b}\:−\:\mathrm{7} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}\:=\:? \\ $$

Question Number 206364    Answers: 2   Comments: 0

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