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AllQuestion and Answers: Page 138

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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$$\:\: \\ $$$$ \\ $$$$ \\ $$$$ . \\ $$$$ \bigtriangleup \\ $$$$ \: \\ $$$$ \\ $$

Question Number 208093 Answers: 1 Comments: 0

lim_(n→∞) (1/n)((a+(1/n))^2 +(a+(2/n))^2 +...+(a+((n−1)/n))^2 )

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\left(\left({a}+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} +\left({a}+\frac{\mathrm{2}}{{n}}\right)^{\mathrm{2}} +...+\left({a}+\frac{{n}−\mathrm{1}}{{n}}\right)^{\mathrm{2}} \right) \\ $$

Question Number 208092 Answers: 0 Comments: 0

Question Number 208083 Answers: 2 Comments: 0

∫_([0,∞]) ((1/x))^(ln(x)) dx

$$\int_{\left[\mathrm{0},\infty\right]} \left(\frac{\mathrm{1}}{{x}}\right)^{{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$

Question Number 208076 Answers: 2 Comments: 0

(5 − ∣x∣)^(− (1/3)) (x^2 − 4) < 0

$$\left(\mathrm{5}\:−\:\mid\mathrm{x}\mid\right)^{−\:\frac{\mathrm{1}}{\mathrm{3}}} \:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right)\:<\:\mathrm{0} \\ $$

Question Number 208075 Answers: 1 Comments: 0

Find: ∫ sin (2x − (π/4)) = ?

$$\mathrm{Find}:\:\:\:\int\:\mathrm{sin}\:\left(\mathrm{2x}\:−\:\frac{\pi}{\mathrm{4}}\right)\:=\:? \\ $$

Question Number 208069 Answers: 1 Comments: 1

F_1 =4N, F_2 =5N, R=8.32N θ=?

$${F}_{\mathrm{1}} =\mathrm{4}{N},\:\:\:{F}_{\mathrm{2}} =\mathrm{5}{N},\:\:\:{R}=\mathrm{8}.\mathrm{32}{N} \\ $$$$\theta=? \\ $$

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