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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

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

Question Number 71000 Answers: 0 Comments: 1

Where f(x)=((4x^2 −1)/(2x−1)) defined in R−{(1/2)}, determine lim_(x→(1/2)) f(x).

$${Where}\:{f}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}\:{defined}\:{in}\: \\ $$$$\mathbb{R}−\left\{\frac{\mathrm{1}}{\mathrm{2}}\right\},\:{determine}\:\underset{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}{f}\left({x}\right). \\ $$

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