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Question Number 92503 Answers: 0 Comments: 3

lim_(x→∞) (e^(10x) −8x)^(1/(2x)) =

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{e}^{\mathrm{10}{x}} −\mathrm{8}{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} \:=\: \\ $$

Question Number 92489 Answers: 0 Comments: 0

(3+((cq)/(12b)))s^2 +((6c)/b)s+(((8c^2 )/(3b^2 ))−b)=0 (1+((cq)/(4b)))s^2 +((3c)/b)(1−((cq)/(12b)))s+(((12c^2 )/b^2 )−b)=0 solve simultaneously for q and s in terms of b and c.

$$\left(\mathrm{3}+\frac{{cq}}{\mathrm{12}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{6}{c}}{{b}}{s}+\left(\frac{\mathrm{8}{c}^{\mathrm{2}} }{\mathrm{3}{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$$\left(\mathrm{1}+\frac{{cq}}{\mathrm{4}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{3}{c}}{{b}}\left(\mathrm{1}−\frac{{cq}}{\mathrm{12}{b}}\right){s}+\left(\frac{\mathrm{12}{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$${solve}\:{simultaneously}\:{for}\:\boldsymbol{{q}}\:{and}\:\boldsymbol{{s}} \\ $$$${in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$

Question Number 92488 Answers: 0 Comments: 11

(3x)^(log_b 3) = (5x)^(log_b 5) x = ?

$$\:\left(\mathrm{3x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{3}} \:=\:\left(\mathrm{5x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{5}} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 92486 Answers: 0 Comments: 0

The smallest interval [a, b] such that ∫_( 0) ^1 (1/(√(1+x^4 ))) dx ∈ [a, b] is given by

$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{interval}\:\left[{a},\:{b}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:{dx}\:\in\:\left[{a},\:{b}\right]\:\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$

Question Number 92484 Answers: 1 Comments: 0

∫_5 ^7 x^2 f ′′′(x) dx =? if f′′(7) = 2 , f′′(5) =1 f′(7) = −2 , f′(5) = −1 f(7)= −3 , f(5) = −4

$$\underset{\mathrm{5}} {\overset{\mathrm{7}} {\int}}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{f}\:'''\left(\mathrm{x}\right)\:\mathrm{dx}\:=? \\ $$$$\mathrm{if}\:\mathrm{f}''\left(\mathrm{7}\right)\:=\:\mathrm{2}\:,\:\mathrm{f}''\left(\mathrm{5}\right)\:=\mathrm{1} \\ $$$$\mathrm{f}'\left(\mathrm{7}\right)\:=\:−\mathrm{2}\:,\:\mathrm{f}'\left(\mathrm{5}\right)\:=\:−\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{7}\right)=\:−\mathrm{3}\:,\:\mathrm{f}\left(\mathrm{5}\right)\:=\:−\mathrm{4}\: \\ $$$$ \\ $$

Question Number 92474 Answers: 0 Comments: 0

please anyone wanna help me with Q91948

$$\mathrm{please}\:\mathrm{anyone}\:\mathrm{wanna}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{Q91948} \\ $$

Question Number 92468 Answers: 1 Comments: 0

y (d^2 y/dx)−9y = 3

$$\mathrm{y}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}}−\mathrm{9y}\:=\:\mathrm{3} \\ $$

Question Number 92465 Answers: 1 Comments: 7

for a 2d vectors if ∣a + b∣ = ∣a−b∣ what relationship does a and b have?

$$\mathrm{for}\:\mathrm{a}\:\mathrm{2d}\:\:\mathrm{vectors}\:\mathrm{if}\:\mid{a}\:+\:{b}\mid\:=\:\mid{a}−{b}\mid\:\mathrm{what}\:\mathrm{relationship}\:\mathrm{does}\:{a}\:\mathrm{and}\:{b}\:\mathrm{have}? \\ $$$$ \\ $$

Question Number 92464 Answers: 0 Comments: 4

(dy/dx) = (e^y /x^2 ) − (1/x)

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{e}^{\mathrm{y}} }{\mathrm{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 92461 Answers: 0 Comments: 1

cos (((3x)/4)−π)=sin ((π/4)−2x) x ∈ [0, π ]

$$\mathrm{cos}\:\left(\frac{\mathrm{3x}}{\mathrm{4}}−\pi\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{2x}\right) \\ $$$$\mathrm{x}\:\in\:\left[\mathrm{0},\:\pi\:\right]\: \\ $$

Question Number 92453 Answers: 0 Comments: 2

(( i))^(1/(i )) ?

$$\sqrt[{\mathrm{i}\:\:}]{\:\mathrm{i}}\:? \\ $$

Question Number 92452 Answers: 0 Comments: 0

(2xy^2 −y)dx = (2x−x^2 y)dy

$$\left(\mathrm{2xy}^{\mathrm{2}} −\mathrm{y}\right)\mathrm{dx}\:=\:\left(\mathrm{2x}−\mathrm{x}^{\mathrm{2}} \mathrm{y}\right)\mathrm{dy}\: \\ $$

Question Number 92448 Answers: 4 Comments: 1

{ ((5^x .6^y = 150)),((5^y .6^x = 180 )) :}

$$\begin{cases}{\mathrm{5}^{\mathrm{x}} .\mathrm{6}^{\mathrm{y}} \:=\:\mathrm{150}}\\{\mathrm{5}^{\mathrm{y}} .\mathrm{6}^{\mathrm{x}} \:=\:\mathrm{180}\:}\end{cases} \\ $$

Question Number 92445 Answers: 1 Comments: 0

Question Number 92438 Answers: 0 Comments: 1

find the domaine and simplify the function f(x)=arcos(((1−x^2 )/(1+x^2 )))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domaine}\:\mathrm{and}\:\mathrm{simplify} \\ $$$$\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arcos}\left(\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right) \\ $$

Question Number 92426 Answers: 0 Comments: 4

If x^2 +2xy=0 find y

$$\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}=\mathrm{0}\:\mathrm{find}\:\mathrm{y} \\ $$

Question Number 92425 Answers: 0 Comments: 1

If A and B are two different number such that A+B=C and A×B=C find A and B.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two} \\ $$$$\mathrm{different}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}+\mathrm{B}=\mathrm{C}\:\mathrm{and}\:\mathrm{A}×\mathrm{B}=\mathrm{C} \\ $$$$\mathrm{find}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$

Question Number 92424 Answers: 0 Comments: 3

If 2x−0i=ϱ^(πi) find the value of x

$$\mathrm{If}\:\mathrm{2x}−\mathrm{0i}=\varrho^{\pi\mathrm{i}} \: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 92423 Answers: 1 Comments: 0

lim_(x⇒∞) ((4(x+3)!−x!)/(x[(x+2)!−(x−1)!]))

$${lim}_{{x}\Rightarrow\infty} \frac{\mathrm{4}\left({x}+\mathrm{3}\right)!−{x}!}{{x}\left[\left({x}+\mathrm{2}\right)!−\left({x}−\mathrm{1}\right)!\right]} \\ $$

Question Number 92422 Answers: 0 Comments: 0

solve (y^2 +yz)dx+(z^2 +xy)dy+(y^2 −xy)dz=0 help me sir

$${solve}\:\left({y}^{\mathrm{2}} +{yz}\right){dx}+\left({z}^{\mathrm{2}} +{xy}\right){dy}+\left({y}^{\mathrm{2}} −{xy}\right){dz}=\mathrm{0} \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 92421 Answers: 1 Comments: 0

∫((cscx)/(cos(2x)+2cos^2 x))dx pleas sir help me

$$\int\frac{{cscx}}{{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}^{\mathrm{2}} {x}}{dx} \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 92420 Answers: 2 Comments: 2

Question Number 92447 Answers: 0 Comments: 1

find ∫_(1/6) ^(1/5) (dx/((√(1−3x))+(√(1+3x))))

$${find}\:\int_{\frac{\mathrm{1}}{\mathrm{6}}} ^{\frac{\mathrm{1}}{\mathrm{5}}} \:\:\frac{{dx}}{\sqrt{\mathrm{1}−\mathrm{3}{x}}+\sqrt{\mathrm{1}+\mathrm{3}{x}}} \\ $$

Question Number 92410 Answers: 0 Comments: 3

find ∫_1 ^(√2) (dx/((√(1+3x))−(√(1−3x))))

$${find}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\mathrm{3}{x}}−\sqrt{\mathrm{1}−\mathrm{3}{x}}} \\ $$

Question Number 92407 Answers: 0 Comments: 0

let f(a) =∫_0 ^1 ln((√(1+x))+a(√(1−x)))dx with a>0 1)explicite f(a) 2)find g(a) =∫_0 ^1 ((√(1−x))/((√(1+x))+a(√(1−x)))) dx 3) find the value of ∫_0 ^1 ln((√(1+x))+2(√(1−x)))dx and ∫_0 ^1 ln((√(1+x))+(1/3)(√(1−x)))dx 4) calculate A(θ) =∫_0 ^1 ln((√(1+x))+sinθ (√(1−x)))dx 0<θ<(π/2)

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}\right){dx}\:\:\:{with}\:\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){explicite}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}−{x}}}{\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\mathrm{2}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$${and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\frac{\mathrm{1}}{\mathrm{3}}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{sin}\theta\:\sqrt{\mathrm{1}−{x}}\right){dx}\: \\ $$$$\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 92399 Answers: 0 Comments: 1

sin^3 (x)+cos^4 (x) = 0

$$\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\mathrm{0} \\ $$

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