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Question Number 110136 Answers: 4 Comments: 0

Question Number 110132 Answers: 0 Comments: 4

lim_(x→0) ((5cos^2 x−2cos x−3)/(cos x−cos 3x)) ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5cos}\:^{\mathrm{2}} {x}−\mathrm{2cos}\:{x}−\mathrm{3}}{\mathrm{cos}\:{x}−\mathrm{cos}\:\mathrm{3}{x}}\:? \\ $$

Question Number 110118 Answers: 1 Comments: 4

prove that ∫_0 ^1 Γ(1−(x/2))Γ(1+(x/2))dx=(4/π)G where G(catalan constant)

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \Gamma\left(\mathrm{1}−\frac{{x}}{\mathrm{2}}\right)\Gamma\left(\mathrm{1}+\frac{{x}}{\mathrm{2}}\right){dx}=\frac{\mathrm{4}}{\pi}{G} \\ $$$${where}\:{G}\left({catalan}\:{constant}\right) \\ $$

Question Number 110119 Answers: 1 Comments: 0

A body of mass 5kg is acted on by two forces 30N and 40N. Find the vector acceleration of the object?

$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{5kg}\:\mathrm{is}\:\mathrm{acted}\:\mathrm{on}\:\mathrm{by}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{30N} \\ $$$$\mathrm{and}\:\mathrm{40N}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{vector}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}? \\ $$

Question Number 110112 Answers: 1 Comments: 0

show that ∫_0 ^∞ xsin(x^3 )dx=(1/3)•(π/(Γ((1/3))))

$${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}\mathrm{sin}\left({x}^{\mathrm{3}} \right){dx}=\frac{\mathrm{1}}{\mathrm{3}}\bullet\frac{\pi}{\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)} \\ $$

Question Number 110109 Answers: 2 Comments: 0

Question Number 110096 Answers: 0 Comments: 8

find the following product integral (1) ∫(x)^dx (2) ∫(e^x )^dx

$${find}\:{the}\:{following}\:{product}\:{integral} \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{1}\right)\:\:\:\:\int\left({x}\right)^{{dx}} \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right)\:\:\:\:\int\left({e}^{{x}} \right)^{{dx}} \\ $$

Question Number 110095 Answers: 3 Comments: 0

[((be)/(math))] lim_(x→0) x^2 cos ((1/x))

$$\:\:\:\left[\frac{{be}}{{math}}\right] \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right) \\ $$

Question Number 110092 Answers: 1 Comments: 0

Question Number 110087 Answers: 0 Comments: 3

Solve the system following of equations { ((x+y+z=2)),((2x+3y+z=1)),((x^2 +(y+2)^2 +(z−1)^2 =9)) :}

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{following}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{2}}\\{\mathrm{2x}+\mathrm{3y}+\mathrm{z}=\mathrm{1}}\\{\mathrm{x}^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{2}\right)^{\mathrm{2}} +\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{9}}\end{cases} \\ $$

Question Number 110086 Answers: 1 Comments: 0

((♠JS♠)/(★■.★)) If lim_(x→a) ((x^2 +2∣ax∣−3a^2 )/( (√x)−(√a) )) = P , with a>0 then the value of lim_(x→a) ((2x^2 −∣ax∣−a^2 )/(x−a)) is ___ (a) ((3P)/(4(√a))) (b) ((3P)/(8(√a))) (c) ((8P)/(3(√a))) (d) ((4P)/(3(√a) )) (e) ((3P)/(8a))

$$\:\:\frac{\spadesuit{JS}\spadesuit}{\bigstar\blacksquare.\bigstar} \\ $$$${If}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}\mid{ax}\mid−\mathrm{3}{a}^{\mathrm{2}} }{\:\sqrt{{x}}−\sqrt{{a}}\:}\:=\:{P}\:,\:{with}\:{a}>\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mid{ax}\mid−{a}^{\mathrm{2}} }{{x}−{a}}\:{is} \\ $$$$\_\_\_ \\ $$$$\:\left({a}\right)\:\frac{\mathrm{3}{P}}{\mathrm{4}\sqrt{{a}}}\:\:\:\:\:\:\left({b}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}\sqrt{{a}}}\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{8}{P}}{\mathrm{3}\sqrt{{a}}} \\ $$$$\:\:\left({d}\right)\:\frac{\mathrm{4}{P}}{\mathrm{3}\sqrt{{a}}\:}\:\:\:\:\left({e}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}{a}} \\ $$

Question Number 110056 Answers: 2 Comments: 0

prove that ∫_(−∞) ^(+∞) ((cos^4 x−6sin^2 xcos^2 x+sin^4 x)/(1+x^2 ))dx=(π/e^4 )

$${prove}\:{that}\: \\ $$$$\int_{−\infty} ^{+\infty} \frac{\mathrm{cos}^{\mathrm{4}} {x}−\mathrm{6sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{4}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi}{{e}^{\mathrm{4}} } \\ $$

Question Number 110050 Answers: 1 Comments: 0