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Question Number 42472 Answers: 0 Comments: 0

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Question Number 42469 Answers: 0 Comments: 0

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Question Number 42463 Answers: 1 Comments: 1

let y =(√(x+(√(x+(√(x+2)))))) calculate (dy/dx)

$${let}\:{y}\:\:=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\mathrm{2}}}} \\ $$$${calculate}\:\:\frac{{dy}}{{dx}} \\ $$

Question Number 42458 Answers: 0 Comments: 0

a boy is in front of a wall.The distance between boy and wall is 12ft.the boy is moving towards the wall in such a way that half the distance between the wall and him is crossed in one minutes.So find the time the boy reach to the wall

$${a}\:{boy}\:{is}\:{in}\:{front}\:{of}\:{a}\:{wall}.{The}\:{distance}\:{between} \\ $$$${boy}\:{and}\:{wall}\:{is}\:\mathrm{12}{ft}.{the}\:{boy}\:{is}\:{moving}\:{towards} \\ $$$${the}\:{wall}\:{in}\:{such}\:{a}\:{way}\:{that}\:\boldsymbol{{half}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{wall}}\:\boldsymbol{{and}}\:\boldsymbol{{him}}\:\boldsymbol{{is}}\:\boldsymbol{{crossed}}\:\boldsymbol{{in}}\:\boldsymbol{{one}} \\ $$$$\boldsymbol{{minutes}}.\boldsymbol{{S}}{o}\:{find}\:{the}\:{time}\:{the}\:{boy}\:{reach}\:{to}\:{the}\:{wall} \\ $$

Question Number 42448 Answers: 3 Comments: 0

Question Number 42446 Answers: 2 Comments: 1

Question Number 42445 Answers: 0 Comments: 0

find A_n = ∫_0 ^(π/4) tan^n t dt with n integer natural .

$${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {t}\:{dt}\:\:\:{with}\:{n}\:{integer}\:{natural}\:. \\ $$

Question Number 42435 Answers: 1 Comments: 1

find ∫_0 ^1 (dx/((√x) +(√(1−x))))

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\sqrt{{x}}\:+\sqrt{\mathrm{1}−{x}}} \\ $$

Question Number 42430 Answers: 1 Comments: 2

find ∫ (dx/(3+tan^2 x))

$${find}\:\int\:\:\:\:\:\:\:\frac{{dx}}{\mathrm{3}+{tan}^{\mathrm{2}} {x}} \\ $$

Question Number 42422 Answers: 1 Comments: 2

Question Number 42408 Answers: 0 Comments: 2

(√(a−(√(a+x ))))+ (√(a+(√(a−x)) )) = 2x Solve for x in terms of a

$$\sqrt{{a}−\sqrt{{a}+{x}\:}}+\:\sqrt{{a}+\sqrt{{a}−{x}}\:}\:=\:\mathrm{2}{x} \\ $$$${Solve}\:{for}\:{x}\:{in}\:{terms}\:{of}\:{a} \\ $$

Question Number 42407 Answers: 1 Comments: 1

∫ (1/(1 + tanx)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tanx}}\:\mathrm{dx} \\ $$

Question Number 42402 Answers: 0 Comments: 0

calculate ∫∫_(x≤x^2 +y^2 ≤1) ((dxdy)/((1+x^2 +y^2 )^2 ))

$${calculate}\:\int\int_{{x}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$

Question Number 42395 Answers: 0 Comments: 1

calculate ∫∫_D ((xy)/((1+x^2 +y^2 )))dxdy with D ={(x,y)∈ R^2 / 0≤x≤1 ,0≤y≤1, x^2 +y^2 ≤1}

$${calculate}\:\int\int_{{D}} \:\:\:\:\:\:\frac{{xy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:/\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1},\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$

Question Number 42394 Answers: 1 Comments: 1

find ∫_0 ^1 (dt/(t+(√(1−t^2 )))) dt

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{t}+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt} \\ $$

Question Number 42392 Answers: 1 Comments: 1

calculate ∫ ((lnx)/(x +x(lnx)^2 ))dx

$${calculate}\:\int\:\:\:\frac{{lnx}}{{x}\:+{x}\left({lnx}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 42391 Answers: 1 Comments: 1

find the value of ∫_0 ^(π/4) ln(1+tanx)dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{tanx}\right){dx} \\ $$

Question Number 42375 Answers: 1 Comments: 5

Find value of α such that the following system has infinite many solutions x − 3z = −3 −2x − αy + z = 2 x + 2y + αz = 1

$$\mathrm{Find}\:\mathrm{value}\:\mathrm{of}\:\:\alpha\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system} \\ $$$$\mathrm{has}\:\mathrm{infinite}\:\mathrm{many}\:\mathrm{solutions} \\ $$$$ \\ $$$${x}\:−\:\mathrm{3}{z}\:=\:−\mathrm{3} \\ $$$$−\mathrm{2}{x}\:−\:\alpha{y}\:+\:{z}\:=\:\mathrm{2} \\ $$$${x}\:+\:\mathrm{2}{y}\:+\:\alpha{z}\:=\:\mathrm{1} \\ $$

Question Number 42374 Answers: 0 Comments: 1

let f(x) = ∫_0 ^∞ arctan(xt^2 )cos(t^2 ) dt 1) find a explicite form of f^′ (x) 2) find a explicite form of f(x) 3) find the value of ∫_0 ^∞ cos(t^2 ) arctan(t^2 )dt and ∫_0 ^∞ cos(t^2 )arctan(2t^2 )dt

$${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:{arctan}\left({xt}^{\mathrm{2}} \right){cos}\left({t}^{\mathrm{2}} \right)\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{cos}\left({t}^{\mathrm{2}} \right)\:{arctan}\left({t}^{\mathrm{2}} \right){dt}\:\:\:{and}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({t}^{\mathrm{2}} \right){arctan}\left(\mathrm{2}{t}^{\mathrm{2}} \right){dt} \\ $$

Question Number 42370 Answers: 1 Comments: 1

Question Number 42367 Answers: 1 Comments: 0

lim_(n→∞) ((( ((n),(0) ) ((n),(1) ) ((n),(2) )... ((n),(n) )))^(1/(n^2 +n)) )

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{{n}^{\mathrm{2}} +{n}}]{\:\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}...\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}}\right) \\ $$

Question Number 42366 Answers: 1 Comments: 0

∫_(2005) ^(2017) (((ln ∣x − 2017∣)^(2017) )/((ln ∣x − 2015∣)^(2017) + (ln ∣x − 2017∣)^(2017) )) dx

$$\underset{\mathrm{2005}} {\overset{\mathrm{2017}} {\int}}\:\frac{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2015}\mid\right)^{\mathrm{2017}} \:+\:\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }\:{dx} \\ $$

Question Number 42364 Answers: 0 Comments: 3

∫ ((x + sinx − cosx − 1)/(x + e^x + sinx)) dx

$$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{sinx}\:−\:\mathrm{cosx}\:−\:\mathrm{1}}{\mathrm{x}\:+\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{sinx}}\:\mathrm{dx} \\ $$

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