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Question Number 69478 Answers: 0 Comments: 1

lim_(n→∞) sin(n𝛑) = ?

$$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}sin}}\left(\boldsymbol{{n}\pi}\right)\:=\:? \\ $$

Question Number 69462 Answers: 0 Comments: 1

find the equation of the circle which ends one of the diameters of two points p_1 (−2,3) and p_2 (4,5)

$$ \\ $$$${find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{which}\:{ends}\:{one}\:{of}\:{the}\:{diameters}\:{of}\:{two}\:{points}\:{p}_{\mathrm{1}} \left(−\mathrm{2},\mathrm{3}\right)\:{and}\:{p}_{\mathrm{2}} \left(\mathrm{4},\mathrm{5}\right) \\ $$

Question Number 69460 Answers: 0 Comments: 1

find the equation of the circle whose center is the origin and touches the line 3x−4y−15=0

$${find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{whose}\:{center}\:{is}\:{the}\:{origin}\:{and}\:{touches}\:{the}\:{line}\:\mathrm{3}{x}−\mathrm{4}{y}−\mathrm{15}=\mathrm{0} \\ $$

Question Number 69459 Answers: 0 Comments: 0

Question Number 69458 Answers: 0 Comments: 1

find the value sin(−13π/6) , cos(49π/4)

$${find}\:{the}\:{value}\:{sin}\left(−\mathrm{13}\pi/\mathrm{6}\right)\:,\:{cos}\left(\mathrm{49}\pi/\mathrm{4}\right) \\ $$$$ \\ $$

Question Number 69457 Answers: 1 Comments: 0

find value log40/9 +4log5 +2log6 ?

$${find}\:{value}\:{log}\mathrm{40}/\mathrm{9}\:\:+\mathrm{4}{log}\mathrm{5}\:\:+\mathrm{2}{log}\mathrm{6}\:\:? \\ $$

Question Number 69456 Answers: 1 Comments: 1

Question Number 69450 Answers: 0 Comments: 0

Question Number 69436 Answers: 1 Comments: 0

Question Number 69433 Answers: 1 Comments: 0

Question Number 69431 Answers: 2 Comments: 0

Question Number 69429 Answers: 0 Comments: 2

Question Number 69423 Answers: 0 Comments: 1

Question Number 69418 Answers: 0 Comments: 0

Question Number 69416 Answers: 1 Comments: 1

Question Number 69413 Answers: 0 Comments: 1

Question Number 69398 Answers: 2 Comments: 1

Question Number 69393 Answers: 0 Comments: 2

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

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

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