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AllQuestion and Answers: Page 138

Question Number 208338 Answers: 0 Comments: 0

Question Number 208335 Answers: 1 Comments: 0

∫_(−1) ^1 (√(1−t^4 ))dt

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{t}^{\mathrm{4}} }{dt} \\ $$

Question Number 208334 Answers: 0 Comments: 1

∫_0 ^(4/π) ln(cosx)dx

$$\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$

Question Number 208332 Answers: 1 Comments: 0

Question Number 208328 Answers: 0 Comments: 0

Question Number 208327 Answers: 1 Comments: 0

Question Number 208322 Answers: 1 Comments: 0

Question Number 208318 Answers: 1 Comments: 0

calcul lim n→+∞ ∫_0 ^(+∞) ((cos(nx))/((nx+1)(1+x^2 ) ))dx

$${calcul}\:\:\:{lim}\:{n}\rightarrow+\infty \\ $$$$\int_{\mathrm{0}} ^{+\infty} \:\frac{{cos}\left({nx}\right)}{\left({nx}+\mathrm{1}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:}{dx} \\ $$

Question Number 208316 Answers: 1 Comments: 0

∫ ((x^2 + 3)/(x^2 (x + 1)(x^2 + 1)^2 )) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{3}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}\:\:+\:\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 208312 Answers: 1 Comments: 0

lim_(x→0 ((a^x −1)/x) = log a)

$${lim}_{{x}\rightarrow\mathrm{0}\:\frac{{a}^{{x}} −\mathrm{1}}{{x}}\:=\:{log}\:{a}} \\ $$

Question Number 208306 Answers: 2 Comments: 1

calcul / lim n→+∞ ∫_0 ^(+∞) f_n (x) f_n (x)= arctan((x/n))e^(−x) dx

$${calcul}\:/\:{lim}\:{n}\rightarrow+\infty\:\int_{\mathrm{0}} ^{+\infty} \:{f}_{{n}} \left({x}\right) \\ $$$$\:{f}_{{n}} \left({x}\right)=\:{arctan}\left(\frac{{x}}{{n}}\right){e}^{−{x}} {dx} \\ $$

Question Number 208303 Answers: 1 Comments: 0

Resolver (∂^2 u/∂y^2 ) − x^2 u = xe^(4y)

$${Resolver} \\ $$$$\frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }\:−\:{x}^{\mathrm{2}} {u}\:=\:{xe}^{\mathrm{4}{y}} \\ $$

Question Number 208293 Answers: 1 Comments: 0

( / ) + ( ^2 / ^2 ) + ( ^2 / ^3 ) + ( ^2 / ^4 ) + ( ^2 / ^5 ) + ...

$$\:\:\:\:\: \frac{ }{ }\:+\:\frac{ ^{\mathrm{2}} }{ ^{\mathrm{2}} }\:+\:\frac{ ^{\mathrm{2}} }{ ^{\mathrm{3}} }\:+\:\frac{ ^{\mathrm{2}} }{ ^{\mathrm{4}} }\:+\:\frac{ ^{\mathrm{2}} }{ ^{\mathrm{5}} }\:+\:...\: \\ $$$$\:\:\:\:\: \\ $$

Question Number 208292 Answers: 1 Comments: 0

let T be a n×n matrix with integral entries and Q = T + (1/2)I where I denote the n×n identity matrix then prove that matrix Q is invertible

$$\:\mathrm{let}\:\mathrm{T}\:\mathrm{be}\:\mathrm{a}\:{n}×{n}\:\mathrm{matrix}\:\mathrm{with}\:\mathrm{integral}\: \\ $$$$\:\mathrm{entries}\:\mathrm{and}\:\:\mathrm{Q}\:=\:\mathrm{T}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{I}\:\:\:\mathrm{where}\:\mathrm{I}\:\mathrm{denote} \\ $$$$\:\:\mathrm{the}\:\mathrm{n}×\mathrm{n}\:\mathrm{identity}\:\mathrm{matrix}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\:\:\mathrm{that}\:\mathrm{matrix}\:\mathrm{Q}\:\mathrm{is}\:\mathrm{invertible} \\ $$

Question Number 208288 Answers: 2 Comments: 0

Question Number 208282 Answers: 1 Comments: 2

If cosα−cosβ = (1/5) sinα + sinβ = (1/2) Find cos(α + β) = ?

$$\mathrm{If}\:\:\:\mathrm{cos}\alpha−\mathrm{cos}\beta\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\mathrm{sin}\alpha\:+\:\mathrm{sin}\beta\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{cos}\left(\alpha\:+\:\beta\right)\:=\:? \\ $$

Question Number 208280 Answers: 1 Comments: 0

L=∫_0 ^(4/π) ln(cosx)dx

$${L}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$

Question Number 208277 Answers: 2 Comments: 0

Question Number 208269 Answers: 2 Comments: 1

Question Number 208264 Answers: 1 Comments: 0

e^x .

$$\:\: \mathrm{e}^{\mathrm{x}} . \\ $$

Question Number 208263 Answers: 1 Comments: 0

Question Number 208259 Answers: 2 Comments: 0

Question Number 208256 Answers: 0 Comments: 1

^2 ((( π)/ )) + ^2 ((( π)/ )) + ^2 ((( π)/ ))=?

$$\: ^{\mathrm{2}} \left(\frac{ \pi}{ }\right)\:+\: ^{\mathrm{2}} \left(\frac{ \pi}{ }\right)\:+\: ^{\mathrm{2}} \left(\frac{ \pi}{ }\right)=? \\ $$

Question Number 208252 Answers: 1 Comments: 0

cos (((2π)/(21)))cos (((4π)/(21)))cos (((8π)/(21)))cos (((10π)/(22)))cos (((16π)/(21)))cos (((20π)/(21)))=?

$$\:\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{8}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{10}\pi}{\mathrm{22}}\right)\mathrm{cos}\:\left(\frac{\mathrm{16}\pi}{\mathrm{21}}\right)\mathrm{cos}\:\left(\frac{\mathrm{20}\pi}{\mathrm{21}}\right)=? \\ $$

Question Number 208251 Answers: 0 Comments: 0

Question Number 208245 Answers: 1 Comments: 0

K=∫_0 ^(4/π) ln(cosx)dx

$${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$

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