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AllQuestion and Answers: Page 139

Question Number 208187 Answers: 1 Comments: 0

Find: 1,03^(200) = ?

$$\mathrm{Find}:\:\:\:\mathrm{1},\mathrm{03}^{\mathrm{200}} \:=\:? \\ $$

Question Number 208178 Answers: 5 Comments: 3

Question Number 208176 Answers: 1 Comments: 1

Find the value of the folloing integral. determinant ((( 𝛀=∫_0 ^( (𝛑/2)) (( 1)/(1 + (( cosx))^(1/3) )) dx = ? )))

$$ \\ $$$$\:\:\:\:\:\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{the}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{folloing}}\:\boldsymbol{{integral}}. \\ $$$$\:\:\:\:\:\:\: \\ $$$$\begin{array}{|c|}{\:\:\:\boldsymbol{\Omega}=\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\mathrm{1}}{\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\:\boldsymbol{{cosx}}}}\:\boldsymbol{{dx}}\:=\:?\:\:}\\\hline\end{array} \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 208173 Answers: 1 Comments: 1

(5/(−∞))=?

$$\frac{\mathrm{5}}{−\infty}=? \\ $$

Question Number 208167 Answers: 2 Comments: 0

y = 3 cos^2 α + 2 cos α find: max(y) = ?

$$\mathrm{y}\:=\:\mathrm{3}\:\mathrm{cos}^{\mathrm{2}} \:\alpha\:+\:\mathrm{2}\:\mathrm{cos}\:\alpha \\ $$$$\mathrm{find}:\:\:\:\mathrm{max}\left(\mathrm{y}\right)\:=\:? \\ $$

Question Number 208164 Answers: 2 Comments: 0

Solve for x: x^2 +x^2 (1−x^2 )+x^2 (1−x^2 )^2 +x^2 (1−x^2 )^3 +...+x^2 (1−x^2 )^(100) =1

$${Solve}\:{for}\:{x}: \\ $$$${x}^{\mathrm{2}} +{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)+{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} +{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} +...+{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{100}} =\mathrm{1} \\ $$

Question Number 208149 Answers: 3 Comments: 0

Question Number 208148 Answers: 2 Comments: 0

Question Number 208139 Answers: 1 Comments: 0

log _(10) (x^3 +x) = log _2 (x)

$$\:\:\: \\ $$$$ \mathrm{log}\:_{\mathrm{10}} \left({x}^{\mathrm{3}} +{x}\right)\:=\:\mathrm{log}\:_{\mathrm{2}} \left({x}\right)\: \\ $$

Question Number 208135 Answers: 1 Comments: 0

a_(n+2) = a_(n+1) + (1/2)a_n a_1 =1 a_2 =2 a_n a_(11)

$$\:\: {a}_{{n}+\mathrm{2}} \:=\:{a}_{{n}+\mathrm{1}} \:+\:\frac{\mathrm{1}}{\mathrm{2}}{a}_{{n}} \: \\ $$$$\:\: {a}_{\mathrm{1}} =\mathrm{1}\: {a}_{\mathrm{2}} =\mathrm{2} \\ $$$$\:\: {a}_{{n}} \: {a}_{\mathrm{11}} \\ $$

Question Number 208134 Answers: 0 Comments: 0

Question Number 208140 Answers: 1 Comments: 0

∫_0 ^π (dx/(1+((sin x))^(1/3) ))=? exact result required

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{dx}}{\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{sin}\:{x}}}=? \\ $$$$\mathrm{exact}\:\mathrm{result}\:\mathrm{required} \\ $$

Question Number 208130 Answers: 1 Comments: 0

(1/(cos x−cos 3x)) + (1/(cos x−cos 5x)) + (1/(cos x−cos 7x)) + (1/(cos x−cos 11x))=?

$$\:\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{3x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{5x}}\:+ \\ $$$$\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{7x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{11x}}=?\: \\ $$

Question Number 208129 Answers: 2 Comments: 0

x^(303) + x^(73) + 1 ∫_1 ^(379) ^(−1) (x)

$$\:\:\:\: \mathrm{x}^{\mathrm{303}} \:+\: \mathrm{x}^{\mathrm{73}} \:+\:\mathrm{1}\: \\ $$$$\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{379}} {\int}} ^{−\mathrm{1}} \left(\mathrm{x}\right)\: \\ $$

Question Number 208128 Answers: 0 Comments: 0

Question Number 208122 Answers: 0 Comments: 0

Question Number 208121 Answers: 0 Comments: 2

Question Number 208111 Answers: 3 Comments: 1

Question Number 208110 Answers: 1 Comments: 0

Question Number 208106 Answers: 1 Comments: 0

Question Number 208105 Answers: 0 Comments: 2

Find: (1/4) + (1/8) + (3/(64)) + (4/(256)) + ... + = ?

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{8}}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{64}}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{256}}\:\:+\:\:...\:\:+\:\:=\:\:? \\ $$

Question Number 208104 Answers: 0 Comments: 0

Question Number 208103 Answers: 1 Comments: 0

Find inf{(m/n) ∣ m, n ∈ N, m<n−2}

$$\mathrm{Find}\:\mathrm{inf}\left\{\frac{{m}}{{n}}\:\mid\:{m},\:{n}\:\in\:\mathbb{N},\:{m}<{n}−\mathrm{2}\right\} \\ $$

Question Number 208100 Answers: 0 Comments: 0

Question Number 208097 Answers: 1 Comments: 0

{ (((x+m)^((x+m)^2 ) = 2)),((2^(x−m) +7 = 2^(x−m+1) −1)) :} x.m .

$$\:\:\: \begin{cases}{\left(\mathrm{x}+\mathrm{m}\right)^{\left(\mathrm{x}+\mathrm{m}\right)^{\mathrm{2}} } \:=\:\mathrm{2}}\\{\mathrm{2}^{\mathrm{x}−\mathrm{m}} \:+\mathrm{7}\:=\:\mathrm{2}^{\mathrm{x}−\mathrm{m}+\mathrm{1}} \:−\mathrm{1}}\end{cases} \\ $$$$\:\:\: {x}.{m}\:. \\ $$

Question Number 208090 Answers: 0 Comments: 0

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