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Question Number 93683 Answers: 1 Comments: 0

∫ (t^2 i +cos 2tj +e^(−t) k) dt

$$\int\:\left(\mathrm{t}^{\mathrm{2}} \boldsymbol{\mathrm{i}}\:+\mathrm{cos}\:\mathrm{2t}\boldsymbol{\mathrm{j}}\:+\mathrm{e}^{−\mathrm{t}} \boldsymbol{\mathrm{k}}\right)\:\mathrm{dt}\: \\ $$

Question Number 93676 Answers: 1 Comments: 1

solve without L′Hopital lim_(x→0) ((5(√(x+1))−2(√(x+4))−1)/x) ?

$$\mathrm{solve}\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5}\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{2}\sqrt{\mathrm{x}+\mathrm{4}}−\mathrm{1}}{\mathrm{x}}\:? \\ $$

Question Number 93648 Answers: 2 Comments: 0

lim_(x→0) ((1−sin 2x)/x^3 ) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\:? \\ $$

Question Number 93636 Answers: 0 Comments: 0

calcilate U_n =∫_0 ^∞ ((sin(nx))/(e^x −1))dx

$${calcilate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{e}^{{x}} −\mathrm{1}}{dx} \\ $$$$ \\ $$

Question Number 93635 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((xsin(πx))/(x^4 +4)) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\pi{x}\right)}{{x}^{\mathrm{4}} \:+\mathrm{4}}\:{dx} \\ $$

Question Number 93634 Answers: 2 Comments: 2

calculate ∫_0 ^∞ (dx/(x^4 +x^2 +1))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 93633 Answers: 0 Comments: 1

calvulate ∫_0 ^∞ ((cos(πx))/(1+x^4 ))dx

$${calvulate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 93632 Answers: 2 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 −3)/((x^2 −x+1)^2 ))dx

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

Question Number 93626 Answers: 1 Comments: 9

Question Number 93638 Answers: 2 Comments: 2

∫ ((x^4 +4x^2 )/(√(x^2 +4))) dx ?

$$\int\:\frac{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} }{\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:?\: \\ $$

Question Number 93623 Answers: 0 Comments: 2

Question Number 93620 Answers: 1 Comments: 0

(3x+3y−4) (dy/dx) = x+y

$$\left(\mathrm{3x}+\mathrm{3y}−\mathrm{4}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}+\mathrm{y}\: \\ $$

Question Number 93618 Answers: 0 Comments: 1

Question Number 93610 Answers: 1 Comments: 0

∫(((√(x^n +1))/x))dx

$$\int\left(\frac{\sqrt{\mathrm{x}^{\mathrm{n}} +\mathrm{1}}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 93587 Answers: 3 Comments: 0

∫((x+1)/(x^2 −((1+(√5))/2)x+1))dx

$$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}}{dx} \\ $$

Question Number 93705 Answers: 0 Comments: 3

find real q so that x^4 −40x^2 +q = 0 has four real solution forming AP.

$$\mathrm{find}\:\mathrm{real}\:\mathrm{q}\:\mathrm{so}\:\mathrm{that}\:\mathrm{x}^{\mathrm{4}} −\mathrm{40x}^{\mathrm{2}} +\mathrm{q}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{four}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{forming} \\ $$$$\mathrm{AP}.\: \\ $$

Question Number 93571 Answers: 0 Comments: 1

Prove that ((1−tan^3 θ)/(1+tan^3 θ)) =1−2sin^2 θ

$${Prove}\:{that}\:\frac{\mathrm{1}−{tan}^{\mathrm{3}} \theta}{\mathrm{1}+{tan}^{\mathrm{3}} \theta}\:=\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \theta \\ $$

Question Number 93569 Answers: 0 Comments: 0

Question Number 93568 Answers: 0 Comments: 1

Question Number 93567 Answers: 1 Comments: 1

Given that A={0,1,3,5} B={1,2,4,7} and C={1,2,3,5,8} prove that (i) (A∩B)∩C = A∩(B∩C) (ii) (A∪B)∪C = A∪(B∪C) (iii) (A∪B)∩C = (A∪C)∪(B∩C) (iv) (A∩C)∪B = (A∪B)∩(C∪B)

$${Given}\:{that}\:{A}=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{5}\right\}\:{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{7}\right\}\:{and}\:{C}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8}\right\}\:{prove}\:{that} \\ $$$$\left(\mathrm{i}\right)\:\left(\mathrm{A}\cap\mathrm{B}\right)\cap\mathrm{C}\:=\:\mathrm{A}\cap\left(\mathrm{B}\cap\mathrm{C}\right) \\ $$$$\left(\mathrm{ii}\right)\:\left(\mathrm{A}\cup\mathrm{B}\right)\cup\mathrm{C}\:=\:\mathrm{A}\cup\left(\mathrm{B}\cup\mathrm{C}\right) \\ $$$$\left(\mathrm{iii}\right)\:\left(\mathrm{A}\cup\mathrm{B}\right)\cap\mathrm{C}\:=\:\left(\mathrm{A}\cup\mathrm{C}\right)\cup\left(\mathrm{B}\cap\mathrm{C}\right) \\ $$$$\left(\mathrm{iv}\right)\:\left(\mathrm{A}\cap\mathrm{C}\right)\cup\mathrm{B}\:=\:\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{C}\cup\mathrm{B}\right) \\ $$

Question Number 93555 Answers: 0 Comments: 3

Question Number 93553 Answers: 0 Comments: 2

∫ln(1+e^u )du

$$\int{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{u}} \right)\mathrm{du} \\ $$

Question Number 93546 Answers: 0 Comments: 13

Which app is the best to evaluate ((W(2 ln 2))/(ln 2))

$$\:\:\mathrm{Which}\:\mathrm{app}\:\mathrm{is}\:\mathrm{the}\:\mathrm{best}\:\mathrm{to}\:\mathrm{evaluate} \\ $$$$\:\:\:\:\frac{\mathrm{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}} \\ $$

Question Number 93540 Answers: 0 Comments: 7

Question Number 93720 Answers: 0 Comments: 2

∫ (dx/((x+1)^3 (√(x^2 +2x))))

$$\int\:\frac{\boldsymbol{{dx}}}{\left(\boldsymbol{{x}}+\mathrm{1}\right)^{\mathrm{3}} \:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}}}\: \\ $$

Question Number 93534 Answers: 1 Comments: 0

A^2 = ((7,3),(9,4) ) ⇒ A = ((a,b),(c,d) ) Find the all of different matrices A (i) . If a, b, c, d ∈ Z (ii) . If a, b, c, d ∈ R^+

$${A}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\mathrm{7}}&{\mathrm{3}}\\{\mathrm{9}}&{\mathrm{4}}\end{pmatrix}\:\:\:\Rightarrow\:\:{A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix} \\ $$$${Find}\:\:{the}\:\:{all}\:\:{of}\:\:\:{different}\:\:{matrices}\:\:{A}\:\: \\ $$$$\left({i}\right)\:.\:{If}\:\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{Z}\:\:\: \\ $$$$\left({ii}\right)\:.\:{If}\:\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{R}^{+} \: \\ $$

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