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∫e^(x^5 +8x^2 ) dx =((√π)/(4(√2)))e^x^5 erfi(2(√2)x)−((5(√π))/(4(128)(√2)))(super−erf_((hyper)) (2(√2)x))+c where[super−erf_((hyper)) (t)] is super−function in D_2 and [D_n ]

$$\int{e}^{{x}^{\mathrm{5}} +\mathrm{8}{x}^{\mathrm{2}} } {dx} \\ $$$$=\frac{\sqrt{\pi}}{\mathrm{4}\sqrt{\mathrm{2}}}{e}^{{x}^{\mathrm{5}} } {erfi}\left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)−\frac{\mathrm{5}\sqrt{\pi}}{\mathrm{4}\left(\mathrm{128}\right)\sqrt{\mathrm{2}}}\left({super}−{erf}_{\left({hyper}\right)} \left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)\right)+{c} \\ $$$$ \\ $$$${where}\left[{super}−{erf}_{\left({hyper}\right)} \left({t}\right)\right]\:{is}\:{super}−{function} \\ $$$${in}\:{D}_{\mathrm{2}} \:{and}\:\left[{D}_{{n}} \right] \\ $$

Question Number 98149 Answers: 1 Comments: 1

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A man arrives at a bus stop in between 12:00pm and 12:15pm. Assuming a bus arrives the bus stop every 15 minutes, find the probability of him getting a bus in less than 5 minutes.

$$\mathcal{A}\:\mathrm{man}\:\mathrm{arrives}\:\mathrm{at}\:\mathrm{a}\:\mathrm{bus}\:\mathrm{stop}\:\mathrm{in}\:\mathrm{between}\:\mathrm{12}:\mathrm{00pm}\:\mathrm{and} \\ $$$$\mathrm{12}:\mathrm{15pm}.\:\mathrm{Assuming}\:\mathrm{a}\:\mathrm{bus}\:\mathrm{arrives}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{stop}\:\mathrm{every} \\ $$$$\mathrm{15}\:\mathrm{minutes},\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{him}\:\mathrm{getting}\:\mathrm{a}\:\mathrm{bus}\:\mathrm{in} \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{5}\:\mathrm{minutes}. \\ $$

Question Number 98137 Answers: 3 Comments: 0

Question Number 98135 Answers: 0 Comments: 2

how to split x^2 +xy+y^2 into ((√3)/2)(x+y)^2 +(1/2)(x−y)^2 ?

$${how}\:{to}\:{split}\:{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \:{into} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\left({x}+{y}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\left({x}−{y}\right)^{\mathrm{2}} \:? \\ $$

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Question Number 98119 Answers: 0 Comments: 1

Find the shortest distance between the skew lines ((x−3)/3) = ((8−y)/1) = ((z−3)/1) and ((x+3)/(−3)) = ((y+7)/2) = ((z−6)/4) .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{skew}\:\mathrm{lines}\:\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\:=\:\frac{\mathrm{8}−\mathrm{y}}{\mathrm{1}}\:=\:\frac{\mathrm{z}−\mathrm{3}}{\mathrm{1}}\:\mathrm{and}\: \\ $$$$\frac{\mathrm{x}+\mathrm{3}}{−\mathrm{3}}\:=\:\frac{\mathrm{y}+\mathrm{7}}{\mathrm{2}}\:=\:\frac{\mathrm{z}−\mathrm{6}}{\mathrm{4}}\:. \\ $$

Question Number 98118 Answers: 1 Comments: 0

calculate Σ_(n=1) ^∞ (ξ(2n)−1)x^(2n) ξ(x)=Σ_(n=1) ^∞ (1/n^x )

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

Question Number 98116 Answers: 0 Comments: 0

prove the compact form of multivariable Taylor series (T∗B)=Σ_(n=1,n=2..n_d =0) ^∞ ((Π_(i=0) ^n_d (x_i −d_i ))/(Π_(i=0) ^n_d (n_i )!)) Π_(i=0) ^n_d (∂/∂x_i )f

$${prove}\:{the}\:{compact}\:{form}\:{of}\:{multivariable} \\ $$$${Taylor}\:{series} \\ $$$$ \\ $$$$\left({T}\ast{B}\right)=\underset{{n}=\mathrm{1},{n}=\mathrm{2}..{n}_{{d}} =\mathrm{0}} {\overset{\infty} {\sum}}\frac{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}} } \left({x}_{\mathrm{i}} −{d}_{\mathrm{i}} \right)}{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}} } \left({n}_{\mathrm{i}} \right)!}\:\underset{\mathrm{i}=\mathrm{0}} {\overset{{n}_{{d}} } {\prod}}\frac{\partial}{\partial{x}_{\mathrm{i}} }{f} \\ $$

Question Number 98114 Answers: 1 Comments: 0

1 lim_(x→∞) ^3 (√(5x^3 )) = ? 2 lim_(x→∞) (1 + (n/(x + 𝛂)))^x ;𝛂 is constant

$$\mathrm{1}\:\:\:\underset{\boldsymbol{{x}}\rightarrow\infty} {\boldsymbol{{lim}}}\:^{\mathrm{3}} \sqrt{\mathrm{5}\boldsymbol{{x}}^{\mathrm{3}} }\:=\:? \\ $$$$\mathrm{2}\:\:\underset{\boldsymbol{{x}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\left(\mathrm{1}\:+\:\frac{\boldsymbol{{n}}}{\boldsymbol{{x}}\:+\:\boldsymbol{\alpha}}\right)^{\boldsymbol{{x}}} ;\boldsymbol{\alpha}\:\boldsymbol{{is}}\:\boldsymbol{{constant}} \\ $$

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