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Question Number 100369 Answers: 1 Comments: 0

aεZ 0<b<1 a+b=(√(20)) b^2 +4b+8(√5)=?

$${a}\epsilon\mathbb{Z}\:\:\:\mathrm{0}<{b}<\mathrm{1}\:\:\:\: \\ $$$${a}+{b}=\sqrt{\mathrm{20}} \\ $$$${b}^{\mathrm{2}} +\mathrm{4}{b}+\mathrm{8}\sqrt{\mathrm{5}}=? \\ $$

Question Number 100368 Answers: 1 Comments: 0

lim_(n→∞) ∫_(−∞) ^∞ cos (x^n ) dx =? where n=2k, k∈N, k≠0

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{−\infty} ^{\infty} \mathrm{cos}\:\left({x}^{{n}} \right)\:{dx}\:=? \\ $$$${where}\:{n}=\mathrm{2}{k},\:{k}\in\mathbb{N},\:{k}\neq\mathrm{0} \\ $$

Question Number 100289 Answers: 0 Comments: 0

lim_(n→∞) Σ_(k=n) ^(2n) sin((π/k)) Riemann′s integral may help

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{n}} {\overset{\mathrm{2n}} {\sum}}\mathrm{sin}\left(\frac{\pi}{\mathrm{k}}\right) \\ $$$${Riemann}'{s}\:{integral}\:{may}\:{help} \\ $$

Question Number 100285 Answers: 1 Comments: 0

Question Number 100290 Answers: 0 Comments: 1

Question Number 100270 Answers: 2 Comments: 0

Question Number 100302 Answers: 0 Comments: 2

(√(3^(−(1/2)) +1)) = ((√(a+1))/3^(−(1/4)) ) . find a ?

$$\sqrt{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{1}}\:=\:\frac{\sqrt{\mathrm{a}+\mathrm{1}}}{\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{4}}} }\:.\:\mathrm{find}\:\mathrm{a}\:? \\ $$

Question Number 100243 Answers: 2 Comments: 0

find laplace transforme of the function f(t)=(a−bt)^2 +cos^2 (wt)? help me sir ?

$${find}\:{laplace}\:{transforme}\:{of}\:{the}\:{function}\: \\ $$$${f}\left({t}\right)=\left({a}−{bt}\right)^{\mathrm{2}} +{cos}^{\mathrm{2}} \left({wt}\right)? \\ $$$$ \\ $$$${help}\:{me}\:{sir}\:? \\ $$

Question Number 100240 Answers: 2 Comments: 9

Find (x,y)∈R such that; ((x+y)/(x^2 −xy+y^2 ))=(7/2) updated from (2/7)→(7/2). Sorry, it was a mistake.

$$\mathrm{Find}\:\:\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}\:\mathrm{such}\:\:\mathrm{that}; \\ $$$$\frac{\mathrm{x}+\mathrm{y}}{\mathrm{x}^{\mathrm{2}} −\mathrm{xy}+\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$ \\ $$$${updated}\:{from}\:\frac{\mathrm{2}}{\mathrm{7}}\rightarrow\frac{\mathrm{7}}{\mathrm{2}}.\:{Sorry},\:{it}\:{was}\:{a}\:{mistake}. \\ $$

Question Number 100237 Answers: 1 Comments: 0

calculate Σ_(k=0) ^n (((−1)^k )/((k+1)^3 ))C_n ^k

$$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\left(\mathrm{k}+\mathrm{1}\right)^{\mathrm{3}} }\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \\ $$

Question Number 100236 Answers: 1 Comments: 0

calculate Σ_(k=0) ^n (C_n ^k /((k+1)^2 ))

$$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} }{\left(\mathrm{k}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 100235 Answers: 0 Comments: 0

calculateΣ_(n=0) ^∞ (−1)^n ∫_1 ^e x^n lnx dx

$$\mathrm{calculate}\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\left(−\mathrm{1}\right)^{\mathrm{n}} \:\int_{\mathrm{1}} ^{\mathrm{e}} \:\mathrm{x}^{\mathrm{n}} \:\mathrm{lnx}\:\mathrm{dx} \\ $$

Question Number 100409 Answers: 0 Comments: 2

Question Number 100223 Answers: 1 Comments: 0

Question Number 100216 Answers: 1 Comments: 2

if I = ∫_0 ^(π/2) ((sin x)/(sin x + cos x))dx = ∫_0 ^(π/2) ((cos x)/(sin x +cos x))dx then I = ??

$$\mathrm{if}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{dx}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}\: \\ $$$$\mathrm{then}\:{I}\:=\:?? \\ $$

Question Number 100215 Answers: 2 Comments: 1

evaluate lim_(n→∞) ∫_1 ^e x^n ln x dx

$$\mathrm{evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{1}} ^{{e}} {x}^{{n}} \mathrm{ln}\:{x}\:{dx}\: \\ $$

Question Number 100207 Answers: 0 Comments: 2

Given an even fuction f(x) such that ∫_(−a) ^a f(x)dx = (√a) ∀a ≥0 find ∫_3 ^4 f(x) dx

$$\mathrm{Given}\:\mathrm{an}\:\mathrm{even}\:\mathrm{fuction}\:{f}\left({x}\right)\:\mathrm{such}\:\mathrm{that}\:\overset{{a}} {\int}_{−{a}} \:{f}\left({x}\right){dx}\:=\:\sqrt{{a}}\:\forall{a}\:\geqslant\mathrm{0} \\ $$$$\mathrm{find}\:\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$

Question Number 100198 Answers: 0 Comments: 1

Question Number 100197 Answers: 0 Comments: 0

Question Number 100193 Answers: 1 Comments: 3

(√(7+2(√(7−2(√(7+2(√(7−2(√(7+...)))))))))) ?

$$\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+...}}}}}\:? \\ $$

Question Number 100191 Answers: 1 Comments: 1

∫ x^2 e^x dx ?

$$\int\:{x}^{\mathrm{2}} \:{e}^{{x}} \:{dx}\:? \\ $$

Question Number 100190 Answers: 0 Comments: 0

∫_0 ^1 ((x^x /((1−x)^(1−x) ))−(((1−x)^(1−x) )/x^x ))dx

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

Question Number 100189 Answers: 1 Comments: 0

∫tan^i xdx

$$\int{tan}^{{i}} {xdx} \\ $$

Question Number 100186 Answers: 0 Comments: 0

Question Number 100184 Answers: 1 Comments: 0

((ydx + xdy)/(1−x^2 y^2 )) + xdx = 0

$$\frac{\mathrm{ydx}\:+\:\mathrm{xdy}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} }\:+\:\mathrm{xdx}\:=\:\mathrm{0} \\ $$

Question Number 100179 Answers: 2 Comments: 0

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