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AllQuestion and Answers: Page 1273

Question Number 86708 Answers: 1 Comments: 0

∫x (√((√2) x−(√(2x^2 −1)))) dx

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

Question Number 86703 Answers: 3 Comments: 6

I=∫(1/(x^4 +1))dx

$${I}=\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 86701 Answers: 0 Comments: 1

find solution 4^(sin x −(1/4)) − (1/(2+(√2))) .2^(sin x) −1 = 0 in x ∈[ 0,2π ]

$$\mathrm{find}\:\mathrm{solution}\: \\ $$$$\mathrm{4}^{\mathrm{sin}\:\mathrm{x}\:−\frac{\mathrm{1}}{\mathrm{4}}} \:−\:\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:.\mathrm{2}^{\mathrm{sin}\:\mathrm{x}} \:−\mathrm{1}\:=\:\mathrm{0}\: \\ $$$$\mathrm{in}\:\mathrm{x}\:\in\left[\:\mathrm{0},\mathrm{2}\pi\:\right]\: \\ $$

Question Number 86684 Answers: 2 Comments: 0

If (1+px+qx^2 )^8 = 1+8x+52x^2 +kx^3 +... find p , q and k.

$$\mathrm{If}\:\left(\mathrm{1}+\mathrm{px}+\mathrm{qx}^{\mathrm{2}} \right)^{\mathrm{8}} \:=\:\mathrm{1}+\mathrm{8x}+\mathrm{52x}^{\mathrm{2}} +\mathrm{kx}^{\mathrm{3}} +... \\ $$$$\mathrm{find}\:\mathrm{p}\:,\:\mathrm{q}\:\mathrm{and}\:\mathrm{k}.\: \\ $$

Question Number 86675 Answers: 1 Comments: 7

lim_(x→∞) ((∫_0 ^1 (1+x^n )^n dx))^(1/n) =?

$$\underset{{x}\rightarrow\infty} {{lim}}\sqrt[{{n}}]{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{{n}} \right)^{{n}} {dx}}=? \\ $$

Question Number 86672 Answers: 0 Comments: 0

show proofs by induction,that ((x_1 +x_2 +....+x_n )/n)≥(x_1 x_2 ....x_n )^(1/n) ∀n=2^k ,k>1 and (x_1 ,x_2 ,x_3 ,.....x_n )>0.

$${show}\:{proofs}\:{by}\:{induction},{that} \\ $$$$\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +....+{x}_{{n}} }{{n}}\geqslant\left({x}_{\mathrm{1}} {x}_{\mathrm{2}} ....{x}_{{n}} \right)^{\frac{\mathrm{1}}{{n}}} \\ $$$$\forall{n}=\mathrm{2}^{{k}} ,{k}>\mathrm{1}\:{and}\:\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} ,.....{x}_{{n}} \right)>\mathrm{0}. \\ $$

Question Number 86671 Answers: 1 Comments: 0

∫sin(x) arcsin(x)

$$\int{sin}\left({x}\right)\:{arcsin}\left({x}\right) \\ $$

Question Number 86668 Answers: 0 Comments: 1

what is P(∣x∣ > 1 ) if x has a PDF of f(x) = { (((1/4) , −2<x<2)),((0 , elsewhere)) :}

$$\mathrm{what}\:\mathrm{is}\:\mathrm{P}\left(\mid\mathrm{x}\mid\:>\:\mathrm{1}\:\right)\:\mathrm{if}\:\mathrm{x}\:\mathrm{has}\:\mathrm{a}\:\mathrm{PDF}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\begin{cases}{\frac{\mathrm{1}}{\mathrm{4}}\:,\:\:−\mathrm{2}<\mathrm{x}<\mathrm{2}}\\{\mathrm{0}\:,\:\mathrm{elsewhere}}\end{cases} \\ $$

Question Number 86663 Answers: 1 Comments: 1

The matrix A satisfying the equation [(1,3),(0,1) ]A = [(1,( 1)),(0,(−1)) ] is

$$\mathrm{The}\:\mathrm{matrix}\:{A}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix}{A}\:=\:\begin{bmatrix}{\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{−\mathrm{1}}\end{bmatrix}\:\mathrm{is} \\ $$

Question Number 86657 Answers: 1 Comments: 0

solve (1+x^3 )dy −x^2 y dx=0 y(1) = 2

$$\mathrm{solve}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\mathrm{dy}\:−\mathrm{x}^{\mathrm{2}} \:\mathrm{y}\:\mathrm{dx}=\mathrm{0} \\ $$$$\mathrm{y}\left(\mathrm{1}\right)\:=\:\mathrm{2} \\ $$

Question Number 86655 Answers: 1 Comments: 0

lim_(x→−1^+ ) (((√π) −(√(arc cos x)))/(√(x+1)))

$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\pi}\:−\sqrt{\mathrm{arc}\:\mathrm{cos}\:\mathrm{x}}}{\sqrt{\mathrm{x}+\mathrm{1}}} \\ $$

Question Number 86646 Answers: 0 Comments: 2

∫_0 ^1 ((ln(1+x))/(x^2 +1))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 86643 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((cos(2ch(x)))/(x^2 +9))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{ch}\left({x}\right)\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 86640 Answers: 1 Comments: 0

Solve the differential equations: (i).x^2 (d^2 y/dx^2 ) − x(dy/dx) + y = log x. (ii). (x+2)^2 (d^2 y/dx^2 ) − 4(x+2)(dy/dx) + 6y = x.

Question Number 86638 Answers: 1 Comments: 0

I=∫((x^3 −2x^2 +7x−1)/((x−3)^3 (x−2)^2 ))dx

$${I}=\int\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{1}}{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 86634 Answers: 1 Comments: 0

Question Number 86627 Answers: 1 Comments: 3

Question Number 86626 Answers: 1 Comments: 2

∫(√(x^2 +4)) dx answer quick pls

$$\int\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\:\mathrm{dx} \\ $$$$\mathrm{answer}\:\mathrm{quick}\:\mathrm{pls} \\ $$

Question Number 86615 Answers: 1 Comments: 2

∫(√(tan x ))dx

$$\int\sqrt{{tan}\:{x}\:}{dx} \\ $$

Question Number 86614 Answers: 1 Comments: 0

ABC is an isocel triangle such as AB=AC=3 and BC=4 α , β , and γ are its angles. Show that cos(((α+β)/2))=sin((γ/2)) Hi sirs...

$${ABC}\:{is}\:{an}\:{isocel}\:{triangle}\:{such}\:{as} \\ $$$${AB}={AC}=\mathrm{3}\:\:{and}\:{BC}=\mathrm{4} \\ $$$$\alpha\:,\:\beta\:,\:{and}\:\gamma\:{are}\:{its}\:{angles}. \\ $$$${Show}\:{that}\:{cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right)={sin}\left(\frac{\gamma}{\mathrm{2}}\right) \\ $$$${Hi}\:{sirs}... \\ $$

Question Number 86613 Answers: 0 Comments: 6

∫_0 ^(1/2) ∫_0 ^(π/2) (1/(ycos(x)+1))dxdy

$$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{{ycos}\left({x}\right)+\mathrm{1}}{dxdy} \\ $$$$ \\ $$

Question Number 86611 Answers: 1 Comments: 0

∫_1 ^e ((ln x)/(x+1))dx

$$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 86610 Answers: 0 Comments: 4

Question Number 86603 Answers: 2 Comments: 2

lim_(x→−1) (e^x /((1+x)^n ))

$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}} }{\left(\mathrm{1}+{x}\right)^{{n}} } \\ $$

Question Number 86602 Answers: 0 Comments: 0

Question Number 86598 Answers: 0 Comments: 1

write out the general summation formula for the maclaurin series expansion for (1/2) (cos x + cosh x)

$$\:\mathrm{write}\:\mathrm{out}\:\mathrm{the}\:\mathrm{general}\:\mathrm{summation}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\:\mathrm{the}\:\mathrm{maclaurin}\:\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{cos}\:{x}\:+\:\mathrm{cosh}\:{x}\right) \\ $$

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