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Question Number 32482 Answers: 0 Comments: 0

find f(x)= ∫_0 ^π ((sin^2 t)/(1−2xcost +x^2 ))dt with ∣x∣<1 .

$${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {t}}{\mathrm{1}−\mathrm{2}{xcost}\:+{x}^{\mathrm{2}} }{dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$

Question Number 32481 Answers: 0 Comments: 0

find ∫_0 ^∞ ((√(t )) −2(√(t+1)) +(√(t+2))) dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\sqrt{{t}\:}\:−\mathrm{2}\sqrt{{t}+\mathrm{1}}\:+\sqrt{\left.{t}+\mathrm{2}\right)}\:{dt}\right. \\ $$

Question Number 32480 Answers: 0 Comments: 1

find ∫_0 ^α (√(tanx)) dx with 0<α<(π/2) .

$${find}\:\:\int_{\mathrm{0}} ^{\alpha} \:\sqrt{{tanx}}\:{dx}\:{with}\:\mathrm{0}<\alpha<\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 32479 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/((x^2 +1)(x^2 +3x +1)))

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}{x}\:+\mathrm{1}\right)} \\ $$

Question Number 32478 Answers: 0 Comments: 1

find ∫_0 ^∞ ln(((1+t^2 )/t^2 ))dt

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\frac{\mathrm{1}+{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} }\right){dt} \\ $$

Question Number 32477 Answers: 0 Comments: 1

calcilate ∫_0 ^1 ((ln(1−x^2 ))/x^2 )dx

$${calcilate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 32492 Answers: 0 Comments: 0

Question Number 32474 Answers: 0 Comments: 0

Question Number 32473 Answers: 0 Comments: 0

Question Number 32472 Answers: 0 Comments: 0

Question Number 32471 Answers: 0 Comments: 0

Question Number 32470 Answers: 0 Comments: 0

lim_(x→∞) x(sec((1/(√x))) − 1)=...

$$\underset{{x}\rightarrow\infty} {{lim}}\:{x}\left({sec}\left(\frac{\mathrm{1}}{\sqrt{{x}}}\right)\:−\:\mathrm{1}\right)=... \\ $$

Question Number 32458 Answers: 0 Comments: 0

For the model of a plane in a wind tunnel, turbulence occurs at a ........ speed for turbulence for an actual plane (greater/smaller).

$${For}\:{the}\:{model}\:{of}\:{a}\:{plane}\:{in}\:{a}\:{wind} \\ $$$${tunnel},\:{turbulence}\:{occurs}\:{at}\:{a}\:........ \\ $$$${speed}\:{for}\:{turbulence}\:{for}\:{an}\:{actual} \\ $$$${plane}\:\left({greater}/{smaller}\right). \\ $$

Question Number 32446 Answers: 1 Comments: 0

Question Number 32444 Answers: 0 Comments: 6

Question Number 32441 Answers: 1 Comments: 0

Question Number 32440 Answers: 1 Comments: 0

Question Number 32524 Answers: 0 Comments: 0

(1/2)x^2 +(√2)=

$$\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}= \\ $$

Question Number 32425 Answers: 0 Comments: 0

( (1/(99)) − 1)^(108) + ((2/(99)) − 1)^(107) + ((3/(99)) − 1)^(106) + ... + (((107)/(99)) − 1)^2 + (((108)/(99)) − 1) = ....

$$\left(\:\frac{\mathrm{1}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{108}} \:+\:\left(\frac{\mathrm{2}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{107}} \:+\:\left(\frac{\mathrm{3}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{106}} \:+\:...\:+\:\left(\frac{\mathrm{107}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\frac{\mathrm{108}}{\mathrm{99}}\:−\:\mathrm{1}\right)\:\:=\:\:\:.... \\ $$

Question Number 32424 Answers: 1 Comments: 0

Question Number 32423 Answers: 0 Comments: 0

Question Number 32420 Answers: 0 Comments: 0

Question Number 32419 Answers: 0 Comments: 0

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Question Number 32418 Answers: 0 Comments: 1

The number of real roots or x^8 − x^5 − x + 1 = 0 is equal to

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{or} \\ $$$${x}^{\mathrm{8}} −\:{x}^{\mathrm{5}} −\:{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 32409 Answers: 1 Comments: 0

Question Number 32407 Answers: 0 Comments: 1

lim_(x→0) ((1−cos (1−cos x))/(x×x×x×x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}} \\ $$

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