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Question Number 29449    Answers: 0   Comments: 0

find lim_(n→+∞) ^ ^n (√(n!)) .n^(−(n+1)) .

$${find}\:{lim}_{{n}\rightarrow+\infty} ^{} \:^{{n}} \sqrt{{n}!}\:.{n}^{−\left({n}+\mathrm{1}\right)} . \\ $$

Question Number 29448    Answers: 0   Comments: 0

find lim_(x→1) ∫_x ^x^2 ((cos(πt))/(ln(t)))dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{cos}\left(\pi{t}\right)}{{ln}\left({t}\right)}{dt}\:. \\ $$

Question Number 29447    Answers: 0   Comments: 0

find A_n = ∫_0 ^∞ (dx/((1+x^2 )^n )) with n from N^★ .

$${find}\:\:\:{A}_{{n}} =\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

Question Number 29446    Answers: 1   Comments: 1

let give a<1 find the value of f(a)= ∫_0 ^(π/2) (dx/(1−acos^2 x)).

$${let}\:{give}\:{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}−{acos}^{\mathrm{2}} {x}}. \\ $$

Question Number 29445    Answers: 1   Comments: 0

find ∫ (dx/(sinx +sin(2x))) .

$${find}\:\:\:\int\:\:\:\:\:\:\:\frac{{dx}}{{sinx}\:+{sin}\left(\mathrm{2}{x}\right)}\:. \\ $$

Question Number 29444    Answers: 0   Comments: 1

find ∫_3 ^4 (dx/(x^3 −2x^2 +x−2)) .

$${find}\:\int_{\mathrm{3}} ^{\mathrm{4}} \:\:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2}}\:. \\ $$

Question Number 29443    Answers: 1   Comments: 0

find ∫_0 ^π ((sinx)/(√(1+sin^2 x)))dx

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sinx}}{\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} {x}}}{dx} \\ $$

Question Number 29442    Answers: 1   Comments: 0

splve the d.e xy^′ =(√(x^2 +y^2 )) +y with x>0

$${splve}\:{the}\:{d}.{e}\:\:\:{xy}^{'} =\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:}\:+{y}\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 29441    Answers: 0   Comments: 1

find ∫ (x^2 /((2−x^2 )(√(1−x^2 ))))dx

$${find}\:\int\:\:\frac{{x}^{\mathrm{2}} }{\left(\mathrm{2}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 29440    Answers: 0   Comments: 0

find ∫_0 ^π ((cosx)/((2+cosx)(3+cosx)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{cosx}}{\left(\mathrm{2}+{cosx}\right)\left(\mathrm{3}+{cosx}\right)}{dx} \\ $$

Question Number 29439    Answers: 1   Comments: 0

find ∫_0 ^π (dx/(2+cosx)) .

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\frac{{dx}}{\mathrm{2}+{cosx}}\:. \\ $$

Question Number 29433    Answers: 1   Comments: 0

4(2x^2 )=8^x

$$\mathrm{4}\left(\mathrm{2x}^{\mathrm{2}} \right)=\mathrm{8}^{\mathrm{x}} \\ $$

Question Number 29420    Answers: 1   Comments: 2

Question Number 29418    Answers: 1   Comments: 1

Question Number 29413    Answers: 1   Comments: 1

Question Number 29415    Answers: 0   Comments: 0

Question Number 29405    Answers: 0   Comments: 1

Fluids

$${Fluids} \\ $$

Question Number 29400    Answers: 2   Comments: 1

Question Number 29384    Answers: 0   Comments: 3

Please can it be proven by another means that ∫tan^2 xdx=tanx+x +c

$${Please}\:{can}\:{it}\:{be}\:{proven}\:{by}\:{another} \\ $$$${means}\:{that}\: \\ $$$$ \\ $$$$\:\:\:\:\:\int\mathrm{tan}\:^{\mathrm{2}} {xdx}={tanx}+{x}\:+{c} \\ $$

Question Number 29424    Answers: 0   Comments: 8

Question Number 29425    Answers: 1   Comments: 1

Question Number 29365    Answers: 1   Comments: 0

the line x+y=2 cuts a circle x^2 +y^(2 ) =4 at two points. find the co−ordinates of points.

$${the}\:{line}\:{x}+{y}=\mathrm{2}\:{cuts}\:{a}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}\:} =\mathrm{4}\:{at}\:{two}\:{points}.\:{find}\:{the}\:{co}−{ordinates}\:{of}\:{points}. \\ $$

Question Number 29364    Answers: 0   Comments: 0

Question Number 29363    Answers: 0   Comments: 1

Question Number 29362    Answers: 1   Comments: 2

Question Number 29360    Answers: 2   Comments: 1

Two stones are thrown up simultaneously from the edge of a cliff 200m high with initial speeds of 15ms^(−1) and 30ms^(−1) . Verify that the graph shown below correctly represents the time variation of the relative position of the second stone with respect to the first.Neglect air resistance and assume that the stones do not rebound.Take g=10m/s^2 . Give the equations of the linear and curved parts of the plot.

$${Two}\:{stones}\:{are}\:{thrown}\:{up}\: \\ $$$${simultaneously}\:{from}\:{the}\:{edge}\:{of} \\ $$$${a}\:{cliff}\:\mathrm{200}{m}\:{high}\:{with}\:{initial} \\ $$$${speeds}\:{of}\:\mathrm{15}{ms}^{−\mathrm{1}} \:{and}\:\mathrm{30}{ms}^{−\mathrm{1}} . \\ $$$${Verify}\:{that}\:{the}\:{graph}\:{shown} \\ $$$${below}\:{correctly}\:{represents}\:{the} \\ $$$${time}\:{variation}\:{of}\:{the}\:{relative} \\ $$$${position}\:{of}\:{the}\:{second}\:{stone} \\ $$$${with}\:{respect}\:{to}\:{the}\:{first}.{Neglect} \\ $$$${air}\:{resistance}\:{and}\:{assume}\:{that} \\ $$$${the}\:{stones}\:{do}\:{not}\:{rebound}.{Take} \\ $$$${g}=\mathrm{10}{m}/{s}^{\mathrm{2}} .\:{Give}\:{the}\:{equations}\:{of} \\ $$$${the}\:{linear}\:{and}\:{curved}\:{parts}\:{of} \\ $$$${the}\:{plot}. \\ $$

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