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Question Number 210839 Answers: 0 Comments: 1

show that ∫_0 ^x e^(xt) e^(−t^2 ) dt=e^(x^2 /4) ∫^x _0 e^(−(t^2 /4))

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{xt}}} \boldsymbol{\mathrm{e}}^{−\mathrm{t}^{\mathrm{2}} } \boldsymbol{\mathrm{dt}}=\boldsymbol{\mathrm{e}}^{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\mathrm{4}}} \underset{\mathrm{0}} {\int}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{e}}^{−\frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\mathrm{4}}} \\ $$$$ \\ $$

Question Number 210836 Answers: 0 Comments: 0

Question Number 210816 Answers: 2 Comments: 1

Question Number 210832 Answers: 2 Comments: 1

If the probability of A solving a question is 1/2 and the probability of B solving the question is 2/3 then the probability of the question being solved is

$$ \\ $$If the probability of A solving a question is 1/2 and the probability of B solving the question is 2/3 then the probability of the question being solved is

Question Number 210809 Answers: 1 Comments: 4

Question Number 210807 Answers: 0 Comments: 0

Question Number 210789 Answers: 1 Comments: 0

Question Number 210788 Answers: 1 Comments: 0

s=Σ_(i=1) ^∞ 2^i 2s=s−1 s=1 ? how to explain it and how to judge which case can use this way

$${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1} \\ $$$${s}=\mathrm{1}\:? \\ $$$$\:{how}\:{to}\:{explain}\:{it} \\ $$$${and}\:{how}\:{to}\:{judge}\:{which}\:{case}\:{can}\:{use}\:{this}\:{way} \\ $$

Question Number 210787 Answers: 6 Comments: 0

{ (( If, D : x^2 +y^( 2) + z^( 2) ≤1)),(( ⇒∫∫_D^ ∫(( x^2 + 2y^( 2) )/(x^2 + 4y^2 +z^2 )) dxdydz=?)) :}

$$ \\ $$$$\:\begin{cases}{\:\:\mathrm{I}{f},\:\mathrm{D}\::\:{x}^{\mathrm{2}} \:+{y}^{\:\mathrm{2}} \:+\:{z}^{\:\mathrm{2}} \leqslant\mathrm{1}}\\{\:\Rightarrow\int\underset{\overset{} {\mathrm{D}}} {\int}\int\frac{\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{y}^{\:\mathrm{2}} }{{x}^{\mathrm{2}} \:+\:\mathrm{4}{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} }\:{dxdydz}=?}\end{cases} \\ $$$$ \\ $$$$ \\ $$

Question Number 210786 Answers: 1 Comments: 0

Question Number 210782 Answers: 0 Comments: 2

How to make 4 out of four 0′s ? HELP PLEASE

$$ \\ $$$$\:\:\:\mathscr{H}{ow}\:{to}\:{make}\:\mathrm{4}\:{out}\:{of}\:{four}\:\:\mathrm{0}'{s}\:? \\ $$$$\:\:\:\mathscr{HELP}\:\mathscr{PLEASE} \\ $$$$ \\ $$

Question Number 210769 Answers: 0 Comments: 1

Question Number 210767 Answers: 2 Comments: 2

Question Number 210765 Answers: 1 Comments: 0

Question Number 210761 Answers: 2 Comments: 7

Question Number 210755 Answers: 0 Comments: 0

Question Number 210754 Answers: 1 Comments: 0

Question Number 210753 Answers: 1 Comments: 0

Question Number 210737 Answers: 1 Comments: 0

f(x)=(x^2 /(x^2 +1)) then f((1/1))+f((2/1))+.....+f(((100)/1))+f((1/2)) +f((2/2))+...+f(((100)/2))+f((1/(100)))+f((2/(100))) +......+f(((100)/(100)))=?

Question Number 210729 Answers: 3 Comments: 0