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Question Number 71147    Answers: 2   Comments: 1

Question Number 71146    Answers: 1   Comments: 1

sin α=((12)/(13)) and α is in the 2nd quadrent. prove cos α=−(5/(13))

$$\mathrm{sin}\:\alpha=\frac{\mathrm{12}}{\mathrm{13}}\:\:\mathrm{and}\:\alpha\:\mathrm{is}\:\mathrm{in}\:\mathrm{the}\:\mathrm{2nd}\:\mathrm{quadrent}. \\ $$$$\mathrm{prove}\:\mathrm{cos}\:\alpha=−\frac{\mathrm{5}}{\mathrm{13}} \\ $$

Question Number 71143    Answers: 0   Comments: 1

let A_n =Σ_(k=0) ^n (1/(3k+1)) calculate A_n interms H_n =Σ_(k=1) ^n (1/k)

$${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{calculate}\:{A}_{{n}} \:{interms}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$

Question Number 71142    Answers: 0   Comments: 1

find ∫(√(x(x+1)(x+2)))dx

$${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$

Question Number 71141    Answers: 0   Comments: 6

(2x)^x =(1/(16))

$$\left(\mathrm{2}{x}\right)^{{x}} =\frac{\mathrm{1}}{\mathrm{16}} \\ $$

Question Number 71134    Answers: 1   Comments: 0

if a, b and c are positive, find: ((a/b))^(log_(10) c) ×((b/c))^(log_(10) a) ×((c/a))^(log_(10) b)

$${if}\:{a},\:{b}\:{and}\:{c}\:{are}\:{positive},\:{find}: \\ $$$$\left(\frac{{a}}{{b}}\right)^{{log}_{\mathrm{10}} {c}} ×\left(\frac{{b}}{{c}}\right)^{{log}_{\mathrm{10}} {a}} ×\left(\frac{{c}}{{a}}\right)^{{log}_{\mathrm{10}} {b}} \\ $$$$ \\ $$

Question Number 71117    Answers: 0   Comments: 0

Question Number 71114    Answers: 0   Comments: 0

Question Number 71096    Answers: 1   Comments: 0

Question Number 71091    Answers: 0   Comments: 3

Question Number 71115    Answers: 1   Comments: 0

Question Number 71089    Answers: 1   Comments: 0

((√((√2)−1)))^x +((√((√2)+1)))^x =4

$$\left(\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}\right)^{\mathrm{x}} +\left(\sqrt{\sqrt{\mathrm{2}}+\mathrm{1}}\right)^{\mathrm{x}} =\mathrm{4} \\ $$

Question Number 71082    Answers: 2   Comments: 0

prove that ∣ (√(∣x∣)) − (√(∣y∣)) ∣ ≤ (√(∣x−y∣))

$${prove}\:{that}\: \\ $$$$ \\ $$$$\mid\:\sqrt{\mid{x}\mid}\:−\:\sqrt{\mid{y}\mid}\:\mid\:\leqslant\:\sqrt{\mid{x}−{y}\mid}\: \\ $$$$ \\ $$

Question Number 71073    Answers: 3   Comments: 4

Question Number 71054    Answers: 0   Comments: 2

Question Number 71053    Answers: 1   Comments: 1

Question Number 71052    Answers: 0   Comments: 2

Question Number 71051    Answers: 0   Comments: 2

Question Number 71050    Answers: 1   Comments: 1

Question Number 71049    Answers: 0   Comments: 2

Question Number 71047    Answers: 0   Comments: 1

Question Number 71046    Answers: 0   Comments: 1

Question Number 71045    Answers: 0   Comments: 1

Question Number 71034    Answers: 0   Comments: 6

Question Number 71016    Answers: 2   Comments: 0

ln (e+ln (e+ln (e+...)))=?

$$\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+\boldsymbol{\mathrm{ln}}\:\left(\boldsymbol{{e}}+...\right)\right)\right)=? \\ $$

Question Number 71014    Answers: 0   Comments: 0

calculate ∫_0 ^∞ e^(−(x^2 +(1/x^2 ))) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)} {dx} \\ $$

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