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Question Number 26402 Answers: 1 Comments: 2

find the nature of the serie Σ_(n=0) ^∝ ((n!)/(1+2^n )) .

$${find}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \frac{{n}!}{\mathrm{1}+\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26401 Answers: 1 Comments: 1

find the sum of Σ_(n=1) ^∝ (1/(n 2^n )) .

$${find}\:{the}\:{sum}\:{of}\:\: \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}\:\:\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26400 Answers: 1 Comments: 0

find the sequence (u_n ) wich verify u_n −2 u_(n−1) +1= 2^n

$${find}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{wich}\:{verify}\:{u}_{{n}} \:−\mathrm{2}\:{u}_{{n}−\mathrm{1}} \:+\mathrm{1}=\:\mathrm{2}^{{n}} \\ $$

Question Number 26399 Answers: 2 Comments: 0

calculate ∫∫ _D cos(x^2 +y^2 )dxdy with D=C(o.(√(π/2))).

$${calculate}\:\:\int\int\:_{{D}} {cos}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}\:\:\:{with}\:\:{D}={C}\left({o}.\sqrt{\frac{\pi}{\mathrm{2}}}\right). \\ $$

Question Number 26398 Answers: 2 Comments: 2

find the value of ∫∫_D x^2 y dxdy on the domain D={(x.y)∈R^2 / x^2 +y^2 −2x≤0 and y≥0}

$${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:{x}^{\mathrm{2}} {y}\:{dxdy}\:\:\:{on}\:{the}\:{domain} \\ $$$${D}=\left\{\left({x}.{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:−\mathrm{2}{x}\leqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$

Question Number 26397 Answers: 2 Comments: 1

find ∫ (dx/(x(√(1+x^2 )))) and calculate ∫_1 ^3 (dx/(x(√(1+x^2 ))))

$${find}\:\int\:\:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{and}\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$

Question Number 26396 Answers: 1 Comments: 1

find the value of ∫_0 ^(1 ) (dx/(x^2 +2x +5)) .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:+\mathrm{5}}\:. \\ $$

Question Number 26395 Answers: 1 Comments: 0

find ∫ (dx/(x(√(x^2 +x−1))))

$${find}\:\:\int\:\:\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{1}}}\:\: \\ $$

Question Number 26382 Answers: 0 Comments: 1

Question Number 26381 Answers: 0 Comments: 9

Question Number 26380 Answers: 0 Comments: 0

Question Number 26389 Answers: 0 Comments: 1

Question Number 26368 Answers: 0 Comments: 1

y=a^(arctg(√x)) derivative ?

$${y}={a}^{\mathrm{arc}{tg}\sqrt{{x}}} \\ $$$${derivative}\:? \\ $$

Question Number 26365 Answers: 0 Comments: 1

y=log_a (x^2 −16)

$${y}=\mathrm{log}_{{a}} \left({x}^{\mathrm{2}} −\mathrm{16}\right) \\ $$

Question Number 26364 Answers: 0 Comments: 1

y=x^2 (x−1)^2 min=? max=? help pls

$${y}={x}^{\mathrm{2}} \left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$${min}=?\:\:\:{max}=? \\ $$$${help}\:{pls} \\ $$

Question Number 26363 Answers: 0 Comments: 1

lim_(x→0) (((√(1+xsin x))−(√(cos 2x)))/(tg^2 (x/2)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{x}\mathrm{sin}\:{x}}−\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{{tg}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}} \\ $$

Question Number 26362 Answers: 0 Comments: 0

find the value of ∫_0 ^∝ e^(−x) lnx dx for that use A_n = ∫_0 ^n (1− (t/n))^(n−1) ln(t) dt .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\propto} {e}^{−{x}} {lnx}\:{dx}\:\:\:{for}\:{that}\:{use} \\ $$$${A}_{{n}} \:\:=\:\:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\:\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {ln}\left({t}\right)\:{dt}\:\:. \\ $$

Question Number 26374 Answers: 1 Comments: 0

show that if arg(((z_1 + z_2 )/(z_1 − z_2 ))) = (π/2) then ∣z_1 ∣ = ∣z_2 ∣

$$\mathrm{show}\:\mathrm{that}\:\:\mathrm{if}\:\:\:\:\mathrm{arg}\left(\frac{\mathrm{z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} }{\mathrm{z}_{\mathrm{1}} \:−\:\mathrm{z}_{\mathrm{2}} }\right)\:=\:\frac{\pi}{\mathrm{2}}\:\:\:\:\mathrm{then}\:\:\:\:\mid\mathrm{z}_{\mathrm{1}} \mid\:=\:\mid\mathrm{z}_{\mathrm{2}} \mid \\ $$

Question Number 26360 Answers: 0 Comments: 1

find the value of ∫_0 ^( ∝ ) ((cos(αx))/(1+x^2 )) dx .

$$\:\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\:\propto\:} \:\frac{{cos}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:. \\ $$

Question Number 26352 Answers: 1 Comments: 0

x(x+9)=(x+3)(x+7)−10

$${x}\left({x}+\mathrm{9}\right)=\left({x}+\mathrm{3}\right)\left({x}+\mathrm{7}\right)−\mathrm{10} \\ $$

Question Number 26348 Answers: 1 Comments: 1

Question Number 26347 Answers: 0 Comments: 0

solve: 5x(1 + (1/(x^2 + y^2 ))) = 12 ..... equation (i) 5y(1 − (1/(x^2 + y^2 ))) = 4 ...... equation (ii)

$$\mathrm{solve}: \\ $$$$\mathrm{5x}\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\right)\:=\:\mathrm{12}\:\:\:\:\:\:\:\:.....\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{5y}\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\right)\:=\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:......\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 26359 Answers: 0 Comments: 2

find lim_(n−>∝) ∫_0 ^n (1−(t/n))^(n−1) dt .

$${find}\:\:\:{lim}_{{n}−>\propto} \:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {dt}\:\:\:. \\ $$

Question Number 26358 Answers: 1 Comments: 0

find the value of ∫_0 ^(π/4) tan^n x dx with n element from N.

$${find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {x}\:{dx}\:\:\:\:{with}\: \\ $$$${n}\:\:{element}\:{from}\:\mathbb{N}. \\ $$

Question Number 26357 Answers: 1 Comments: 1

find the value of ∫_0 ^(π/2) ln(cosθ)dθ and ∫_0 ^(π/2) ln(sinθ)dθ .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({cos}\theta\right){d}\theta\:\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({sin}\theta\right){d}\theta\:\:\:. \\ $$

Question Number 26329 Answers: 1 Comments: 0

A small particle moving with a uniform acceleration a covers distances X and Y in the first two equal and consecutive intervals of time t. Show that a = ((Y − X)/t^2 )

$$\mathrm{A}\:\mathrm{small}\:\mathrm{particle}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{a}\:\mathrm{covers}\:\mathrm{distances}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{and}\:\mathrm{consecutive}\:\mathrm{intervals}\:\mathrm{of}\:\mathrm{time}\:\mathrm{t}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{a}\:=\:\frac{\mathrm{Y}\:−\:\mathrm{X}}{\mathrm{t}^{\mathrm{2}} } \\ $$

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