Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1153

Question Number 99120    Answers: 0   Comments: 2

prove that: ∫_(−(1/2)) ^∞ e^(−(4x^6 +12x^5 +15x^4 +10x^3 +4x^2 +x)) dx =((e)^(1/8) /3)[((Γ((1/6))^((−1)/2) )/(2(2)^(1/3) ))1F2(_(1/3,2/3) ^(1/6) ∣((−1)/(69/2)) ) +((Γ(5/6))/(128(4)^(1/3) ))1F2(_(4/3,5/3) ^(5/6) ∣((−1)/(69/2))) −((√π)/(16))12(_(2/3,4/3) ^(1/2) ∣((−1)/(69/2)))

$${prove}\:{that}: \\ $$$$\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\infty} {e}^{−\left(\mathrm{4}{x}^{\mathrm{6}} +\mathrm{12}{x}^{\mathrm{5}} +\mathrm{15}{x}^{\mathrm{4}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{x}\right)} {dx} \\ $$$$=\frac{\sqrt[{\mathrm{8}}]{{e}}}{\mathrm{3}}\left[\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{1}/\mathrm{3},\mathrm{2}/\mathrm{3}} ^{\mathrm{1}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\:\right)\:+\frac{\Gamma\left(\mathrm{5}/\mathrm{6}\right)}{\mathrm{128}\sqrt[{\mathrm{3}}]{\mathrm{4}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{4}/\mathrm{3},\mathrm{5}/\mathrm{3}} ^{\mathrm{5}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:−\frac{\sqrt{\pi}}{\mathrm{16}}\mathrm{12}\left(_{\mathrm{2}/\mathrm{3},\mathrm{4}/\mathrm{3}} ^{\mathrm{1}/\mathrm{2}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:\right. \\ $$

Question Number 99118    Answers: 4   Comments: 0

Question Number 99117    Answers: 1   Comments: 0

let a,b,c ∈R determine the minimum value ((3a)/(b+c))+((4b)/(a+c))+((5c)/(a+b))

$${let}\:{a},{b},{c}\:\in\mathbb{R}\:{determine}\:{the}\:{minimum} \\ $$$${value} \\ $$$$ \\ $$$$\frac{\mathrm{3}{a}}{{b}+{c}}+\frac{\mathrm{4}{b}}{{a}+{c}}+\frac{\mathrm{5}{c}}{{a}+{b}} \\ $$

Question Number 99114    Answers: 1   Comments: 0

calculate: ∫(√x)sinh^(−1) (x)dx where sinh^(−1) (x) is the inverse hyperbolic sine function

$${calculate}: \\ $$$$\int\sqrt{{x}}{sinh}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$${where}\:{sinh}^{−\mathrm{1}} \left({x}\right)\:{is}\:{the}\:{inverse}\:{hyperbolic}\: \\ $$$${sine}\:{function} \\ $$$$ \\ $$$$ \\ $$

Question Number 99113    Answers: 2   Comments: 0

solve y^(′′) +5y^′ −3y =x^2 sin(3x) with y(0) =0 and y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:−\mathrm{3y}\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{3x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 99102    Answers: 0   Comments: 21

Question Number 99097    Answers: 0   Comments: 1

Hello verry nice day for all of you god bless You pleas Can you use black Color shen You post Quation or Give answer is verry hard to read withe other colors

$${Hello}\: \\ $$$${verry}\:{nice}\:{day}\:{for}\:{all}\:{of}\:{you}\:{god}\:{bless}\:{You} \\ $$$${pleas}\:{Can}\:{you}\:{use}\:{black}\:{Color}\:{shen}\:{You}\:{post}\:{Quation}\: \\ $$$${or}\:{Give}\:{answer}\:{is}\:{verry}\:{hard}\:{to}\:{read}\:{withe}\:{other}\:{colors} \\ $$

Question Number 99095    Answers: 1   Comments: 0

Question Number 99094    Answers: 1   Comments: 0

find ((9+9((9+9((9+9((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) − (√(8−(√(8−(√(8+(√(8−(√(8−(√(8−(√(8−(√)))))))...))))))))

$$\mathrm{find}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}− \\ $$$$\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}+\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{}}}}...}}}}\: \\ $$

Question Number 99089    Answers: 1   Comments: 0

((9+((9+((9+((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) −(√(8−(√(8−(√(8−(√(8−...))))))))

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−...}}}} \\ $$

Question Number 99077    Answers: 2   Comments: 2

Question Number 99072    Answers: 2   Comments: 0

Question Number 99058    Answers: 0   Comments: 6

Find a number that becomes N times smaller if the first digit is removed in the following cases: 1) N=17 2) N=27 3)N=37 4)N=47.

$${Find}\:{a}\:{number}\:{that}\:{becomes}\:{N}\:{times} \\ $$$${smaller}\:{if}\:{the}\:{first}\:{digit}\:{is}\:{removed} \\ $$$${in}\:{the}\:{following}\:{cases}: \\ $$$$\left.\mathrm{1}\right)\:{N}=\mathrm{17} \\ $$$$\left.\mathrm{2}\right)\:{N}=\mathrm{27} \\ $$$$\left.\mathrm{3}\right){N}=\mathrm{37} \\ $$$$\left.\mathrm{4}\right){N}=\mathrm{47}. \\ $$

Question Number 99057    Answers: 0   Comments: 0

Find a perfect number that starts with 31415.

$${Find}\:{a}\:{perfect}\:{number}\:{that}\:{starts} \\ $$$${with}\:\mathrm{31415}. \\ $$

Question Number 99055    Answers: 1   Comments: 4

What is the domain of f(x)=arcosh(((1+x^2 )/(1−x^2 ))) ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arcosh}\left(\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)\:? \\ $$

Question Number 99050    Answers: 1   Comments: 2

5^(5−3x) + 2^(x+5) = 5^(7−3x) −2^(x+6)

$$\mathrm{5}^{\mathrm{5}−\mathrm{3}{x}} \:+\:\mathrm{2}^{{x}+\mathrm{5}} \:=\:\mathrm{5}^{\mathrm{7}−\mathrm{3}{x}} \:−\mathrm{2}^{{x}+\mathrm{6}} \: \\ $$

Question Number 99045    Answers: 1   Comments: 0

{ ((x^2 +y^2 = 10)),((x^2 −5xy+6y^2 = 0)) :} find x &y

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{10}}\\{\mathrm{x}^{\mathrm{2}} −\mathrm{5xy}+\mathrm{6y}^{\mathrm{2}} \:=\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\mathrm{y}\: \\ $$

Question Number 99044    Answers: 3   Comments: 0

∫(1/(x^2 +1))dx=?

$$\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}=? \\ $$

Question Number 99025    Answers: 2   Comments: 4

Question Number 99023    Answers: 0   Comments: 3

Question Number 99011    Answers: 1   Comments: 2

Question Number 99007    Answers: 2   Comments: 0

Let I_y = ∫_(−2) ^2 [y^3 cos ((y/2)) + (1/2)]((√(4−y^2 )) ) dy then I_y = ???

$$\mathrm{Let}\:{I}_{{y}} \:=\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\left[{y}^{\mathrm{3}} \:\mathrm{cos}\:\left(\frac{{y}}{\mathrm{2}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right]\left(\sqrt{\mathrm{4}−{y}^{\mathrm{2}} }\:\right)\:{dy}\: \\ $$$$\mathrm{then}\:{I}_{{y}} \:=\:??? \\ $$

Question Number 99005    Answers: 2   Comments: 0

Σ_(m = 1) ^∞ Σ_(n = 1) ^∞ (1/(mn(m+n))) ?

$$\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{mn}\left(\mathrm{m}+\mathrm{n}\right)}\:?\: \\ $$

Question Number 99003    Answers: 3   Comments: 0

Given 5x−3y=6 . find min value of (x−1)^2 +(y+1)^2 ?

$${Given}\:\mathrm{5}{x}−\mathrm{3}{y}=\mathrm{6}\:.\:{find}\:{min}\:{value} \\ $$$${of}\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \:? \\ $$

Question Number 98993    Answers: 1   Comments: 0

Use the laplace tranform to solve (d^2 y/dx^2 ) + 5(dy/dx) + 6y = e^(−x) for y = 0, and (dy/dx) = 1 when x = 0

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{tranform}\:\mathrm{to}\:\mathrm{solve}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{5}\frac{{dy}}{{dx}}\:+\:\mathrm{6}{y}\:=\:{e}^{−{x}} \\ $$$$\mathrm{for}\:\:{y}\:=\:\mathrm{0},\:\mathrm{and}\:\frac{{dy}}{{dx}}\:=\:\mathrm{1}\:\mathrm{when}\:{x}\:=\:\mathrm{0} \\ $$

Question Number 98988    Answers: 1   Comments: 0

Find the tangent at the poles for the polar equation r = a sin 2θ.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{at}\:\mathrm{the}\:\mathrm{poles}\:\mathrm{for}\:\mathrm{the}\:\mathrm{polar} \\ $$$$\mathrm{equation}\:{r}\:=\:{a}\:\mathrm{sin}\:\mathrm{2}\theta. \\ $$

  Pg 1148      Pg 1149      Pg 1150      Pg 1151      Pg 1152      Pg 1153      Pg 1154      Pg 1155      Pg 1156      Pg 1157   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com