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Question Number 10571 Answers: 0 Comments: 0

Question Number 10570 Answers: 0 Comments: 0

n(A)=12 n(B)=10 ⇒min(n(A−B−B^′ ))

$${n}\left({A}\right)=\mathrm{12} \\ $$$${n}\left({B}\right)=\mathrm{10} \\ $$$$\Rightarrow{min}\left({n}\left({A}−{B}−{B}^{'} \right)\right) \\ $$

Question Number 10566 Answers: 2 Comments: 0

Question Number 10564 Answers: 1 Comments: 0

Prove that: lim_(ε→0) ((−1+x^ε )/ε) = ln(x)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{1}+{x}^{\epsilon} }{\epsilon}\:=\:\mathrm{ln}\left({x}\right) \\ $$

Question Number 10563 Answers: 0 Comments: 0

can someone explain to me big K notation? (I don′t know the name) It is related to continuous fractions. e.g. x=b_0 +K_(i=1) ^∞ (a_i /b_i ) e^x =(x^0 /(0!))+(x^1 /(1!))+(x^2 /(2!))+... e^x =Σ_(i=0) ^∞ (x^i /(i!)) =1+(x/(1−((1x)/(2+x−((2x)/(3+x−((3x)/(...)))))))) How do you interperate this in big K notation?

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{explain}\:\mathrm{to}\:\mathrm{me} \\ $$$$\mathrm{big}\:\mathrm{K}\:\mathrm{notation}?\:\left(\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{name}\right) \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{related}\:\mathrm{to}\:\mathrm{continuous}\:\mathrm{fractions}. \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:{x}={b}_{\mathrm{0}} +\underset{{i}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\mathrm{K}}}}\frac{{a}_{{i}} }{{b}_{{i}} } \\ $$$$\: \\ $$$${e}^{{x}} =\frac{{x}^{\mathrm{0}} }{\mathrm{0}!}+\frac{{x}^{\mathrm{1}} }{\mathrm{1}!}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+... \\ $$$${e}^{{x}} =\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{i}} }{{i}!} \\ $$$$\:\:\:\:\:=\mathrm{1}+\frac{{x}}{\mathrm{1}−\frac{\mathrm{1}{x}}{\mathrm{2}+{x}−\frac{\mathrm{2}{x}}{\mathrm{3}+{x}−\frac{\mathrm{3}{x}}{...}}}} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{interperate}\:\mathrm{this}\:\mathrm{in} \\ $$$$\mathrm{big}\:\mathrm{K}\:\mathrm{notation}? \\ $$

Question Number 10562 Answers: 0 Comments: 0

x= [(x_1 ),(x_2 ),(( ⋮)),(x_n ) ] y= [(y_1 ),(y_2 ),(( ⋮)),(y_n ) ] x, y ∈ R^n 1. Prove the length of the vector x, denoted ∣∣x∣∣, is equal to (√(x_1 ^2 +x_2 ^2 +...+x_n ^2 )) 2. Determine if ∣∣x−y∣∣=∣∣y−x∣∣

$$\boldsymbol{{x}}=\begin{bmatrix}{{x}_{\mathrm{1}} }\\{{x}_{\mathrm{2}} }\\{\:\vdots}\\{{x}_{{n}} }\end{bmatrix}\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{y}}=\begin{bmatrix}{{y}_{\mathrm{1}} }\\{{y}_{\mathrm{2}} }\\{\:\vdots}\\{{y}_{{n}} }\end{bmatrix}\:\:\:\:\:\:\:\:\boldsymbol{{x}},\:\boldsymbol{{y}}\:\in\:\mathbb{R}^{{n}} \\ $$$$\: \\ $$$$\mathrm{1}.\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{{x}},\:\mathrm{denoted}\:\mid\mid\boldsymbol{{x}}\mid\mid, \\ $$$$\:\:\:\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\sqrt{{x}_{\mathrm{1}} ^{\mathrm{2}} +{x}_{\mathrm{2}} ^{\mathrm{2}} +...+{x}_{{n}} ^{\mathrm{2}} } \\ $$$$\mathrm{2}.\:\mathrm{Determine}\:\mathrm{if}\:\:\:\mid\mid\boldsymbol{{x}}−\boldsymbol{{y}}\mid\mid=\mid\mid\boldsymbol{{y}}−\boldsymbol{{x}}\mid\mid \\ $$

Question Number 10555 Answers: 0 Comments: 0

why Γ(x)=∫_0 ^1 [−ln(u)]^(x−1) du ? I don′t know how to prove this

$$\mathrm{why}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \left[−\mathrm{ln}\left(\mathrm{u}\right)\right]^{{x}−\mathrm{1}} {du}\:\:? \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{this} \\ $$

Question Number 10553 Answers: 0 Comments: 0

(D^2 +4)y=tan 2x D=d/dx

$$\left(\mathrm{D}^{\mathrm{2}} +\mathrm{4}\right)\mathrm{y}=\mathrm{tan}\:\mathrm{2x}\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}=\mathrm{d}/\mathrm{dx} \\ $$

Question Number 11178 Answers: 0 Comments: 1

If the sum of p terms of an AP is q and the sum of q terms is p, then the sum of p+q terms will be

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:{p}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{is}\:{q}\:\mathrm{and}\: \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:{q}\:\mathrm{terms}\:\mathrm{is}\:{p},\:\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$${p}+{q}\:\:\mathrm{terms}\:\mathrm{will}\:\mathrm{be} \\ $$

Question Number 11172 Answers: 1 Comments: 0

Tangent to the curve (x+y)^3 =(x−y+2)^2 at (−1,1).

$$\mathrm{Tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} =\left(\mathrm{x}−\mathrm{y}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\mathrm{at}\:\left(−\mathrm{1},\mathrm{1}\right). \\ $$

Question Number 11183 Answers: 1 Comments: 0

Question Number 10547 Answers: 1 Comments: 0

A man can row a boat at 4 km/hr in still water. He rows the boat 2km upstream and 2km back to his starting place in 2 hours. How fast is the stream flowing ?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{at}\:\mathrm{4}\:\mathrm{km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}. \\ $$$$\mathrm{He}\:\mathrm{rows}\:\mathrm{the}\:\mathrm{boat}\:\mathrm{2km}\:\mathrm{upstream}\:\mathrm{and}\:\mathrm{2km}\:\mathrm{back}\:\mathrm{to} \\ $$$$\mathrm{his}\:\mathrm{starting}\:\mathrm{place}\:\mathrm{in}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{fast}\:\mathrm{is}\:\mathrm{the}\:\mathrm{stream} \\ $$$$\mathrm{flowing}\:? \\ $$

Question Number 11206 Answers: 3 Comments: 0