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AllQuestion and Answers: Page 117

Question Number 210855 Answers: 3 Comments: 0

Question Number 210843 Answers: 1 Comments: 0

Question Number 210842 Answers: 1 Comments: 0

Question Number 210851 Answers: 1 Comments: 1

Question Number 210840 Answers: 1 Comments: 0

Prove that if x, y are rational numbers satisfying the equation x^5 + y^5 = 2(x^2)(y^2) then 1 - xy is the square of rational number

$$ \\ $$Prove that if x, y are rational numbers satisfying the equation x^5 + y^5 = 2(x^2)(y^2) then 1 - xy is the square of rational number

Question Number 210824 Answers: 0 Comments: 0

Question Number 210820 Answers: 2 Comments: 0

prove ∫_0 ^∞ ((arctan (√(x^2 +2)))/((x^2 +1)(√(x^2 +2)))) dx=(π^2 /(12))

$$\mathrm{prove} \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{arctan}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$

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)))=?

Pg 112 Pg 113 Pg 114 Pg 115 Pg 116 Pg 117 Pg 118 Pg 119 Pg 120 Pg 121

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