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AllQuestion and Answers: Page 1411

Question Number 69429 Answers: 0 Comments: 2

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Question Number 69416 Answers: 1 Comments: 1

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Question Number 69398 Answers: 2 Comments: 1

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Question Number 69390 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ (((1+x)^α −(1+x)^((β) )/x)dx and determine its value

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{x}\right)^{\alpha} −\left(\mathrm{1}+{x}\right)^{\left(\beta\right.} }{{x}}{dx} \\ $$$${and}\:{determine}\:{its}\:{value} \\ $$

Question Number 69389 Answers: 0 Comments: 0

find ∫_(∣z+i∣=3) ((sinz)/(z+i))dz

$${find}\:\int_{\mid{z}+{i}\mid=\mathrm{3}} \:\:\frac{{sinz}}{{z}+{i}}{dz} \\ $$

Question Number 69379 Answers: 0 Comments: 1

calculste f(a) =∫_(−∞) ^(+∞) (((−1)^x^2 )/(x^2 +a^2 ))dx with a>0

$${calculste}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 69377 Answers: 0 Comments: 0

sove x^2 y^′ −(x^3 +1)y =sin(2x)

$${sove}\:\:{x}^{\mathrm{2}} {y}^{'} \:\:−\left({x}^{\mathrm{3}} \:+\mathrm{1}\right){y}\:\:={sin}\left(\mathrm{2}{x}\right) \\ $$

Question Number 69376 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+1)^3 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 69375 Answers: 0 Comments: 0

let f(α) =∫_0 ^∞ ((cos(α(1+x^2 )))/(1+x^2 ))dx 1)determine a explicit form of f(α) 2) calculate ∫_0 ^∞ ((cos(2+2x^2 ))/(x^2 +1))dx

$${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\alpha\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}+\mathrm{2}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 69374 Answers: 0 Comments: 1

let S_n =Σ_(k=1) ^n (((−1)^k )/k) 1) calculate S_n interms of n 2) find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{S}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

Question Number 69373 Answers: 0 Comments: 2

x^3 −3x−3

$${x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{3} \\ $$

Question Number 69585 Answers: 0 Comments: 0

Question Number 69355 Answers: 1 Comments: 0

Find the maximun and minimum values of the function f(x)=x^2 −8x+7 and sketch its graph

$$ \\ $$$${Find}\:{the}\:{maximun}\:{and}\:{minimum}\: \\ $$$${values}\:{of}\:{the}\:{function}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{7} \\ $$$${and}\:{sketch}\:{its}\:{graph}\: \\ $$

Question Number 69347 Answers: 1 Comments: 0

If a well is dug 21m deep and 1.4m in radius, how much earth is dug out from it? If the inner wall of well is plastered at Rupees 20 per m^2 . WHAT WILL BE ITS COST ?

$${If}\:{a}\:{well}\:{is}\:{dug}\:\mathrm{21}{m}\:{deep}\:{and}\:\mathrm{1}.\mathrm{4}{m} \\ $$$${in}\:{radius},\:{how}\:{much}\:{earth}\:{is}\:{dug} \\ $$$${out}\:{from}\:{it}?\:{If}\:{the}\:{inner}\:{wall}\:{of} \\ $$$${well}\:{is}\:{plastered}\:{at}\:\:{Rupees}\:\mathrm{20}\: \\ $$$${per}\:{m}^{\mathrm{2}} .\:{WHAT}\:\:\mathbb{WILL}\:\:{BE}\:\:{ITS} \\ $$$$\mathcal{COST}\:? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 69338 Answers: 1 Comments: 1

Question Number 69412 Answers: 1 Comments: 1

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Question Number 69328 Answers: 0 Comments: 1

∫_( 0) ^(π/2) ((φ(x))/(φ(x)+φ((π/2) −x))) dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\phi\left({x}\right)}{\phi\left({x}\right)+\phi\left(\frac{\pi}{\mathrm{2}}\:−{x}\right)}\:{dx}\:= \\ $$

Question Number 69482 Answers: 1 Comments: 1

lim_(n→∞) ((2+cosn)/(4n+sinn)) = ?

$$\underset{{n}\rightarrow\infty} {{lim}}\frac{\mathrm{2}+{cosn}}{\mathrm{4}{n}+{sinn}}\:=\:? \\ $$

Question Number 74637 Answers: 1 Comments: 1

1)calculate f(x)=∫_0 ^1 t^2 (√(x^2 +t^2 ))dt with x>0 2) calculste g(x)=∫_0 ^1 (t^2 /(√(x^2 +t^2 )))dt

$$\left.\mathrm{1}\right){calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculste}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}^{\mathrm{2}} }{\sqrt{{x}^{\mathrm{2}} +{t}^{\mathrm{2}} }}{dt} \\ $$

Question Number 69319 Answers: 0 Comments: 4

Show that lim_((x,y)→(0,0)) (3/(x^2 + 2y^2 )) does not exist

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\frac{\mathrm{3}}{{x}^{\mathrm{2}} \:+\:\mathrm{2}{y}^{\mathrm{2}} } \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$

Question Number 69385 Answers: 2 Comments: 0

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