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1+2−3−4+5+6−7−8+9+10−11−12+ ... +100 =?

$$\mathrm{1}+\mathrm{2}−\mathrm{3}−\mathrm{4}+\mathrm{5}+\mathrm{6}−\mathrm{7}−\mathrm{8}+\mathrm{9}+\mathrm{10}−\mathrm{11}−\mathrm{12}+ \\ $$$$...\:+\mathrm{100}\:=? \\ $$

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prove ((d )/dx) x^n =nx^(n−1) for all ε>0 Exist δ>0 such that 0<∣x−ξ∣<δ Implies ∣((f(x)−f(ξ))/(x−ξ))−f^((1)) (ξ)∣<ε let′s f(x)=x^n ∀ε>0 , ∃δ>0 such that 0<∣x−ξ∣<δ → ∣((x^n −ξ^n )/(x−ξ))−nξ^(n−1) ∣<ε help me... :(

$$\mathrm{prove}\:\:\frac{\mathrm{d}\:\:\:}{\mathrm{d}{x}}\:{x}^{{n}} ={nx}^{{n}−\mathrm{1}} \\ $$$$\mathrm{for}\:\mathrm{all}\:\epsilon>\mathrm{0}\:\mathrm{Exist}\:\delta>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\mathrm{0}<\mid{x}−\xi\mid<\delta\:\:\mathrm{Implies}\:\mid\frac{{f}\left({x}\right)−{f}\left(\xi\right)}{{x}−\xi}−{f}^{\left(\mathrm{1}\right)} \left(\xi\right)\mid<\epsilon \\ $$$$\mathrm{let}'\mathrm{s}\:{f}\left({x}\right)={x}^{{n}} \: \\ $$$$\forall\epsilon>\mathrm{0}\:,\:\exists\delta>\mathrm{0}\:\mathrm{such}\:\mathrm{that}\:\mathrm{0}<\mid{x}−\xi\mid<\delta\:\rightarrow\:\mid\frac{{x}^{{n}} −\xi^{{n}} }{{x}−\xi}−{n}\xi^{{n}−\mathrm{1}} \mid<\epsilon \\ $$$$\mathrm{help}\:\mathrm{me}...\:\::\left(\:\right. \\ $$

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∀ε>0 , ∃δ>0 s.t ∣x∣<δ ⇒ ∣((sin(x))/x)−1∣<ε δ=??

$$\forall\epsilon>\mathrm{0}\:,\:\exists\delta>\mathrm{0}\:\mathrm{s}.\mathrm{t}\:\:\mid{x}\mid<\delta\:\Rightarrow\:\mid\frac{\mathrm{sin}\left({x}\right)}{{x}}−\mathrm{1}\mid<\epsilon \\ $$$$\delta=?? \\ $$

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{ ((log_3 x=a)),((log_3 y=b)) :} ⇒ log_3 (x^3 ∙y^2 )=?

$$\begin{cases}{\mathrm{log}_{\mathrm{3}} \mathrm{x}=\mathrm{a}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{y}=\mathrm{b}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{x}^{\mathrm{3}} \centerdot\mathrm{y}^{\mathrm{2}} \right)=? \\ $$

Question Number 227466 Answers: 0 Comments: 0

Explain how the following conversions take place.Give the necessary conditions (a)methane to tetra chloromethane (b)Ethanol to acetaldehyde (c)Alchol to ethane

$${Explain}\:{how}\:{the}\:{following} \\ $$$${conversions}\:{take}\:{place}.{Give} \\ $$$${the}\:{necessary}\:{conditions} \\ $$$$\left({a}\right){methane}\:{to}\:{tetra}\:{chloromethane} \\ $$$$\left({b}\right){Ethanol}\:{to}\:{acetaldehyde} \\ $$$$\left({c}\right){Alchol}\:{to}\:{ethane} \\ $$

Question Number 227465 Answers: 2 Comments: 0

How many hydrogen atoms are there in 2.57×10^(−6) g of hydrogen

$${How}\:{many}\:{hydrogen}\:{atoms}\:{are} \\ $$$${there}\:{in}\:\mathrm{2}.\mathrm{57}×\mathrm{10}^{−\mathrm{6}} {g}\:\:{of}\:{hydrogen} \\ $$

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∫ x^dx

$$\int\:{x}^{{dx}} \\ $$

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Let f(x)= { (((1/q) x=(p/q) , p,q∈Z , gcd(p,q)=1 , q>0)),((0 x∈R\Q)) :} 1. Show that f(x) is continuous function when x∈R\Q 2. Show that f(x) is not a continuous function when x∈Q 3. Prove function g(x) does not exist when g(x) is a function that is continuous only in x∈Q 4. ∫_( R) f(x)dx

$$\mathrm{Let}\:{f}\left({x}\right)=\begin{cases}{\frac{\mathrm{1}}{{q}}\:\:\:\:\:{x}=\frac{{p}}{{q}}\:,\:{p},{q}\in\mathbb{Z}\:,\:\mathrm{gcd}\left({p},{q}\right)=\mathrm{1}\:,\:{q}>\mathrm{0}}\\{\mathrm{0}\:\:\:\:{x}\in\mathbb{R}\backslash\mathbb{Q}}\end{cases} \\ $$$$\: \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{when}\:{x}\in\mathbb{R}\backslash\mathbb{Q} \\ $$$$\mathrm{2}.\:\mathrm{Show}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{when}\:{x}\in\mathbb{Q} \\ $$$$\mathrm{3}.\:\mathrm{Prove}\:\mathrm{function}\:\mathrm{g}\left({x}\right)\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$$$\mathrm{when}\:\mathrm{g}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{that}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{only}\:\mathrm{in}\:{x}\in\mathbb{Q} \\ $$$$\mathrm{4}.\:\int_{\:\mathbb{R}} \:{f}\left({x}\right)\mathrm{d}{x} \\ $$

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