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AllQuestion and Answers: Page 347

Question Number 184346    Answers: 1   Comments: 0

∫ ((xdx)/(a+bx)) = ?

$$\:\:\int\:\frac{{xdx}}{{a}+{bx}}\:=\:? \\ $$

Question Number 184341    Answers: 1   Comments: 1

lim_(x→∞) (x^2 /3^x )=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{x}^{\mathrm{2}} }{\mathrm{3}^{{x}} }=? \\ $$

Question Number 184331    Answers: 0   Comments: 0

Question Number 184329    Answers: 3   Comments: 0

lim_(x→0) ((tan^(−1) (p+x)−tan^(−1) (p−x))/x)=?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left({p}+{x}\right)−\mathrm{tan}^{−\mathrm{1}} \left({p}−{x}\right)}{{x}}=? \\ $$

Question Number 184320    Answers: 0   Comments: 4

All-time Universal Formula determinant (((OLD+1=NEW))) Year:-The above formula applies every year. Month:-It also applies every month. Day:-It also applies every day. .... Second:-It also applies every second. ... SO, along with Happy New Year! also: Happy New Month! Happy New Day! .... Happy New Second! ...

$$\boldsymbol{\mathrm{All}}-\boldsymbol{\mathrm{time}}\:\boldsymbol{\mathrm{Universal}}\:\boldsymbol{\mathrm{Formula}} \\ $$$$\:\begin{array}{|c|}{\boldsymbol{\mathrm{OLD}}+\mathrm{1}=\boldsymbol{\mathrm{NEW}}}\\\hline\end{array}\: \\ $$$$\boldsymbol{{Year}}:-\boldsymbol{\mathcal{T}{he}}\:\boldsymbol{{above}}\:\boldsymbol{{formula}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\:\boldsymbol{{year}}. \\ $$$$\boldsymbol{{Month}}:-\boldsymbol{{It}}\:\boldsymbol{{also}}\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{month}}. \\ $$$$\boldsymbol{{Day}}:-\boldsymbol{{It}}\:\boldsymbol{{also}}\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\:\boldsymbol{{day}}. \\ $$$$.... \\ $$$$\boldsymbol{{Second}}:-\boldsymbol{{It}}\:\boldsymbol{{also}}\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\:\:\boldsymbol{{second}}. \\ $$$$... \\ $$$$\boldsymbol{\mathrm{SO}}, \\ $$$$\boldsymbol{\mathrm{along}}\:\boldsymbol{\mathrm{with}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Happy}}\:\boldsymbol{\mathrm{New}}\:\boldsymbol{\mathrm{Year}}! \\ $$$$\boldsymbol{\mathrm{also}}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Happy}}\:\boldsymbol{\mathrm{New}}\:\boldsymbol{\mathrm{Month}}! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Happy}}\:\boldsymbol{\mathrm{New}}\:\boldsymbol{\mathrm{Day}}! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:.... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Happy}}\:\boldsymbol{\mathrm{New}}\:\boldsymbol{\mathrm{Second}}! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:... \\ $$$$ \\ $$

Question Number 184311    Answers: 1   Comments: 0

Question Number 184310    Answers: 0   Comments: 0

Question Number 184307    Answers: 1   Comments: 0

Show that the boundary−value problem y′′+λy=0 y(0)=0, y(L)=0 has only the trival solution y=0 for the cases λ=0 and λ<0. let L be a non−zero real number. ?

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{boundary}−\mathrm{value} \\ $$$$\mathrm{problem}\:\mathrm{y}''+\lambda\mathrm{y}=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}, \\ $$$$\mathrm{y}\left(\mathrm{L}\right)=\mathrm{0}\:\mathrm{has}\:\mathrm{only}\:\mathrm{the}\:\mathrm{trival}\:\mathrm{solution} \\ $$$$\mathrm{y}=\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{cases}\:\lambda=\mathrm{0}\:\mathrm{and}\:\lambda<\mathrm{0}. \\ $$$$\mathrm{let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{zero}\:\mathrm{real}\:\mathrm{number}. \\ $$$$ \\ $$$$ \\ $$$$? \\ $$

Question Number 184306    Answers: 1   Comments: 0

Consider the boundary value problem y^(′′) −2y′+2y=0, y(a)=c ,y(b)=d. 1) If this problem has a unique solution, how are a and b related? 2) If this problem has no solution, how are a,b,c and d related? Help!

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{value}\: \\ $$$$\mathrm{problem}\:\mathrm{y}^{''} −\mathrm{2y}'+\mathrm{2y}=\mathrm{0},\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{a}\right)=\mathrm{c} \\ $$$$,\mathrm{y}\left(\mathrm{b}\right)=\mathrm{d}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique} \\ $$$$\mathrm{solution},\:\mathrm{how}\:\mathrm{are}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{related}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}, \\ $$$$\mathrm{how}\:\mathrm{are}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{related}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184305    Answers: 1   Comments: 0

if: f(x) = x^2 + 2x find x: f(f(f(x + 2))) = 99 999 999

$${if}:\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x} \\ $$$${find}\:{x}: \\ $$$$\:{f}\left({f}\left({f}\left({x}\:+\:\mathrm{2}\right)\right)\right)\:=\:\mathrm{99}\:\mathrm{999}\:\mathrm{999}\: \\ $$

Question Number 184304    Answers: 2   Comments: 0

Question Number 184302    Answers: 1   Comments: 0

Question Number 184287    Answers: 2   Comments: 0

If the area enclosed between the curves y=x² and the line y = 2x is rotated round the x-axis through 4 right angles, find the volume of the solid generated

If the area enclosed between the curves y=x² and the line y = 2x is rotated round the x-axis through 4 right angles, find the volume of the solid generated

Question Number 184280    Answers: 1   Comments: 13

Given { ((a_0 =1)),((a_(n+1) =(1/2)(3a_n +(√(5a_n ^2 −4)) ))) :} ∀n≥0 , n∈I find a_n .

$$\:\:{Given}\:\begin{cases}{{a}_{\mathrm{0}} =\mathrm{1}}\\{{a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}{a}_{{n}} +\sqrt{\mathrm{5}{a}_{{n}} ^{\mathrm{2}} −\mathrm{4}}\:\right)}\end{cases} \\ $$$$\:\forall{n}\geqslant\mathrm{0}\:,\:{n}\in{I}\: \\ $$$$\:\:{find}\:{a}_{{n}} . \\ $$

Question Number 184270    Answers: 2   Comments: 0

((−64))^(1/6) ∙((−128))^(1/7) =?

$$\sqrt[{\mathrm{6}}]{−\mathrm{64}}\centerdot\sqrt[{\mathrm{7}}]{−\mathrm{128}}=? \\ $$

Question Number 184264    Answers: 1   Comments: 0

Question Number 184260    Answers: 3   Comments: 0

x+(1/x)=−1 x^(1377) =?

$$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=−\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{1377}} =? \\ $$

Question Number 184258    Answers: 2   Comments: 0

2yz−4z+2x−2=0 2xz−2z+2y−4=0 2xy−4x−2y+2z+4=0 how to find the all values of the (x,y,z) ?

$$\:\:\:\mathrm{2yz}−\mathrm{4z}+\mathrm{2x}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xz}−\mathrm{2z}+\mathrm{2y}−\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xy}−\mathrm{4x}−\mathrm{2y}+\mathrm{2z}+\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:? \\ $$

Question Number 184251    Answers: 6   Comments: 0

If x (√y) = 2904 Find: y=?

$$\mathrm{If}\:\:\:\mathrm{x}\:\sqrt{\mathrm{y}}\:=\:\mathrm{2904} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}=? \\ $$

Question Number 184242    Answers: 1   Comments: 0

Question Number 184240    Answers: 2   Comments: 1

Question Number 184239    Answers: 1   Comments: 0

f(x)= { ((x−2 if x>3)),((3 if x=3)),((−x+4 if 1≤x<3)),((1 if 1<x)) :} faind lim_(x→1) f(x)=? and lim_(x→3) f(x)=?

$${f}\left({x}\right)=\begin{cases}{{x}−\mathrm{2}\:\:\:\:\:\:\:{if}\:\:{x}>\mathrm{3}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:{x}=\mathrm{3}}\\{−{x}+\mathrm{4}\:\:\:\:{if}\:\:\mathrm{1}\leqslant{x}<\mathrm{3}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:\mathrm{1}<{x}}\end{cases} \\ $$$${faind}\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=?\:\:{and}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$

Question Number 184628    Answers: 0   Comments: 0

Question Number 184626    Answers: 1   Comments: 0

∫_0 ^(+oo) ((artan(2x)−arctan(x))/x)dx

$$\int_{\mathrm{0}} ^{+{oo}} \:\frac{{artan}\left(\mathrm{2}{x}\right)−{arctan}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 184629    Answers: 0   Comments: 0

Question Number 184223    Answers: 0   Comments: 2

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