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AllQuestion and Answers: Page 290

Question Number 189205    Answers: 0   Comments: 6

Question Number 189463    Answers: 1   Comments: 0

Question Number 189145    Answers: 6   Comments: 0

pleas solve this 1) lim_(x→1) ((e^(x+2x+3x+4x+∙∙∙∙∙+nx) −e^((n(n+1))/2) )/(x−1))=? 2) lim_(x→1) ((e^(2^x ∙3^x ∙4^x ∙∙∙∙n^x ) −e^(n!) )/(x−1))=? 3)lim_(x→1) ((e^(x+x^2 +x^3 +.......+x^n ) −e^n )/(x−1))=?

$${pleas}\:{solve}\:{this} \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}+\mathrm{2}{x}+\mathrm{3}{x}+\mathrm{4}{x}+\centerdot\centerdot\centerdot\centerdot\centerdot+{nx}} −{e}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} }{{x}−\mathrm{1}}=? \\ $$$$\left.\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{\mathrm{2}^{{x}} \centerdot\mathrm{3}^{{x}} \centerdot\mathrm{4}^{{x}} \centerdot\centerdot\centerdot\centerdot{n}^{{x}} } −{e}^{{n}!} }{{x}−\mathrm{1}}=? \\ $$$$\left.\mathrm{3}\right)\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.......+{x}^{{n}} } −{e}^{{n}} }{{x}−\mathrm{1}}=? \\ $$

Question Number 189144    Answers: 0   Comments: 1

∫_0 ^( 1) ∫_0 ^( 1) ∫_0 ^( 1) ((√(x + y + z))/( (√x) + (√y) + (√z) )) dxdydz

$$\: \\ $$$$\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\sqrt{{x}\:+\:{y}\:+\:{z}}}{\:\sqrt{{x}}\:+\:\sqrt{{y}}\:+\:\sqrt{{z}}\:}\:{dxdydz} \\ $$$$\: \\ $$$$\: \\ $$

Question Number 189140    Answers: 2   Comments: 0

Question Number 189135    Answers: 2   Comments: 0

Question Number 189137    Answers: 0   Comments: 2

It is known that x is rational x (√(28 + 3(√(28 + 3(√(28 + 3(√?))))))) Find the dufference of possible vaules of x

$$\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\:\mathrm{x}\:\:\mathrm{is}\:\mathrm{rational} \\ $$$$\mathrm{x}\:\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{?}}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dufference}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{vaules} \\ $$$$\mathrm{of}\:\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 189133    Answers: 1   Comments: 0

Convert hexadecimal number 4 A F_(16) to decimal

$$\mathrm{Convert}\:\mathrm{hexadecimal}\:\mathrm{number} \\ $$$$\mathrm{4}\:\mathrm{A}\:\mathrm{F}_{\mathrm{16}} \:\:\mathrm{to}\:\mathrm{decimal} \\ $$

Question Number 189131    Answers: 2   Comments: 0

Question Number 189127    Answers: 3   Comments: 0

Question Number 189126    Answers: 1   Comments: 0

Question Number 189125    Answers: 2   Comments: 0

Question Number 189124    Answers: 1   Comments: 0

Question Number 189123    Answers: 2   Comments: 0

Question Number 189132    Answers: 1   Comments: 0

Find the value of a+b+c+d+e in the system of equations: { ((13a+2b+c+6d+2e=96)),((5a+9b+2c+7d+3e=75)),((7a+8b+17c+11d+7e=99)),((3a+3b+3c+d+8e=55)),((a+7b+6c+4d+9e=79)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{13a}+\mathrm{2b}+\mathrm{c}+\mathrm{6d}+\mathrm{2e}=\mathrm{96}}\\{\mathrm{5a}+\mathrm{9b}+\mathrm{2c}+\mathrm{7d}+\mathrm{3e}=\mathrm{75}}\\{\mathrm{7a}+\mathrm{8b}+\mathrm{17c}+\mathrm{11d}+\mathrm{7e}=\mathrm{99}}\\{\mathrm{3a}+\mathrm{3b}+\mathrm{3c}+\mathrm{d}+\mathrm{8e}=\mathrm{55}}\\{\mathrm{a}+\mathrm{7b}+\mathrm{6c}+\mathrm{4d}+\mathrm{9e}=\mathrm{79}}\end{cases} \\ $$

Question Number 189114    Answers: 2   Comments: 0

Question Number 189112    Answers: 0   Comments: 3

Question Number 189110    Answers: 0   Comments: 1

Question Number 189101    Answers: 0   Comments: 1

Question Number 189079    Answers: 1   Comments: 0

Question Number 189077    Answers: 0   Comments: 0

Question Number 189070    Answers: 1   Comments: 0

Question Number 189066    Answers: 2   Comments: 0

Given f(x)+∫_0 ^1 (x+y)^2 f(y) dy=2x^2 −3x+1 find f(x).

$$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)+\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \:\mathrm{f}\left(\mathrm{y}\right)\:\mathrm{dy}=\mathrm{2x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1} \\ $$$$\:\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$

Question Number 189057    Answers: 0   Comments: 6

Help! Evaluate the following integral usings Green theorem: ∮4xydx + x^2 dy Where C is the square of vertices (0,0), (0,2), (2,0) and (2,2).

$$\: \\ $$$$\:\mathrm{Help}! \\ $$$$\: \\ $$$$\:\mathrm{Evaluate}\:\:\mathrm{the}\:\:\mathrm{following}\:\:\mathrm{integral}\:\:\mathrm{usings}\:\:\mathrm{Green}\:\mathrm{theorem}: \\ $$$$\: \\ $$$$\:\oint\mathrm{4xy}{d}\mathrm{x}\:\:+\:\:\mathrm{x}^{\mathrm{2}} {d}\mathrm{y} \\ $$$$\: \\ $$$$\:\mathrm{Where}\:\:{C}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{square}\:\:\mathrm{of}\:\:\mathrm{vertices}\:\:\left(\mathrm{0},\mathrm{0}\right),\:\left(\mathrm{0},\mathrm{2}\right),\:\left(\mathrm{2},\mathrm{0}\right)\:\:\mathrm{and}\:\:\left(\mathrm{2},\mathrm{2}\right). \\ $$$$\: \\ $$

Question Number 189054    Answers: 1   Comments: 0

Question Number 189053    Answers: 3   Comments: 0

find f(x) 1:f(((x+1)/(x−1)))=x+3; x≠1 2:f(((2x+1)/(x−1)))=x^2 +2x ;x≠1 3:f(x+1)+f(x−y)=2f(x)cosy ∀x,y f(0)=f((π/2))=1

$${find}\:{f}\left({x}\right) \\ $$$$\mathrm{1}:{f}\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}+\mathrm{3};\:{x}\neq\mathrm{1} \\ $$$$\mathrm{2}:{f}\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:;{x}\neq\mathrm{1} \\ $$$$\mathrm{3}:{f}\left({x}+\mathrm{1}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){cosy}\:\forall{x},{y} \\ $$$${f}\left(\mathrm{0}\right)={f}\left(\frac{\pi}{\mathrm{2}}\right)=\mathrm{1} \\ $$

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