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Question Number 192584 Answers: 0 Comments: 0

Question Number 192582 Answers: 1 Comments: 5

Question Number 192580 Answers: 0 Comments: 0

This might be helpful: How to easily calculate z_1 ^z_2 with z_1 , z_2 ∈C: Transform z_1 =re^(iθ) and z_2 =a+bi ⇒ z_1 ^z_2 =(re^(iθ) )^(a+bi) z_1 ^z_2 =r^(a+bi) e^(−bθ+iaθ) z_1 ^z_2 =r^a e^(−bθ) r^(bi) e^(iaθ) z_1 ^z_2 =(r^a /e^(bθ) )e^(i(aθ+bln r))

$$\mathrm{This}\:\mathrm{might}\:\mathrm{be}\:\mathrm{helpful}: \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{easily}\:\mathrm{calculate}\:{z}_{\mathrm{1}} ^{{z}_{\mathrm{2}} } \:\mathrm{with}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\in\mathbb{C}: \\ $$$$\mathrm{Transform}\:{z}_{\mathrm{1}} ={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{and}\:{z}_{\mathrm{2}} ={a}+{b}\mathrm{i}\:\Rightarrow \\ $$$${z}_{\mathrm{1}} ^{{z}_{\mathrm{2}} } =\left({r}\mathrm{e}^{\mathrm{i}\theta} \right)^{{a}+{b}\mathrm{i}} \\ $$$${z}_{\mathrm{1}} ^{{z}_{\mathrm{2}} } ={r}^{{a}+{b}\mathrm{i}} \mathrm{e}^{−{b}\theta+\mathrm{i}{a}\theta} \\ $$$${z}_{\mathrm{1}} ^{{z}_{\mathrm{2}} } ={r}^{{a}} \mathrm{e}^{−{b}\theta} {r}^{{b}\mathrm{i}} \mathrm{e}^{\mathrm{i}{a}\theta} \\ $$$${z}_{\mathrm{1}} ^{{z}_{\mathrm{2}} } =\frac{{r}^{{a}} }{\mathrm{e}^{{b}\theta} }\mathrm{e}^{\mathrm{i}\left({a}\theta+{b}\mathrm{ln}\:{r}\right)} \\ $$

Question Number 192560 Answers: 1 Comments: 3

Question Number 192572 Answers: 0 Comments: 0

Let ABCD be a rectangle having an area of 290. Let E be on BC such that BE : BC = 3 : 2. Let F be on CD such that CF : FD = 3 : 1. If G is the intersection of AE and BF, compute the area of △BEG.

$$\mathrm{Let}\:\:{ABCD}\:\:\mathrm{be}\:\:\mathrm{a}\:\:\mathrm{rectangle}\:\:\mathrm{having}\:\:\mathrm{an}\:\mathrm{area}\:\:\mathrm{of}\:\:\mathrm{290}. \\ $$$$\mathrm{Let}\:\:{E}\:\:\mathrm{be}\:\:\mathrm{on}\:\:{BC}\:\:\mathrm{such}\:\:\mathrm{that}\:\:{BE}\::\:{BC}\:=\:\mathrm{3}\::\:\mathrm{2}. \\ $$$$\mathrm{Let}\:\:{F}\:\:\mathrm{be}\:\:\mathrm{on}\:\:{CD}\:\:\mathrm{such}\:\:\mathrm{that}\:\:{CF}\::\:{FD}\:=\:\mathrm{3}\::\:\mathrm{1}. \\ $$$$\mathrm{If}\:\:{G}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{intersection}\:\:\mathrm{of}\:\:{AE}\:\:\mathrm{and}\:\:{BF},\:\:\mathrm{compute} \\ $$$$\mathrm{the}\:\:\mathrm{area}\:\:\mathrm{of}\:\:\bigtriangleup{BEG}. \\ $$

Question Number 192570 Answers: 2 Comments: 0

Question Number 192573 Answers: 0 Comments: 0

solve; lim_(x→0) x^2 tan(((sinπx)/(2x))) solution let L=lim_(x→0) x^2 tan(((sinπx)/(2x))) since sinx∼x−(x^3 /6) L=lim_(x→0) x^2 tan(((πx)/(2x))−((π^3 x^3 )/(12x))) L=lim_(x→0) x^2 tan((π/2)−((π^3 x^2 )/(12))) since tan((π/2)−x)=(1/(tanx)) L=lim_(x→0) (x^2 /(tan(((π^3 x^2 )/(12))))) L=lim_(x→0) (((π^3 x^2 )/(12))/(tan(((π^3 x^2 )/(12))))) ((12)/π^3 ) L=((12)/π^3 )lim_(x→0) (((π^3 x^2 )/(12))/(tan(((π^3 x^2 )/(12))))) since lim_(x→0) (x/(tanx))=1 L=((12)/π^3 ) ∙1=((12)/π^3 ) solved by HY a.k.a senestro

Question Number 192550 Answers: 1 Comments: 0

how can find the sum Σ_(i=1) ^r (2v_i +1) ?

$${how}\:{can}\:{find}\:{the}\:{sum}\:\underset{{i}=\mathrm{1}} {\overset{{r}} {\sum}}\left(\mathrm{2}{v}_{{i}} +\mathrm{1}\right)\:? \\ $$

Question Number 192549 Answers: 2 Comments: 0

lim_(x→0) x^2 tan (((sin πx)/(2x))) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{\mathrm{sin}\:\pi\mathrm{x}}{\mathrm{2x}}\right)\:=? \\ $$

Question Number 192544 Answers: 0 Comments: 1

If f(t) = 2(e^t − 1) a) Does f(t) exists for all n ? b) If it exist, does it converge ? c) If the sequence converge, does the limit converge ? d) Is the solution uniques ?

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{t}\right)\:=\:\mathrm{2}\left(\mathrm{e}^{\mathrm{t}} \:−\:\mathrm{1}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Does}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{exists}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:? \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{it}\:\mathrm{exist},\:\mathrm{does}\:\mathrm{it}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{c}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{converge},\:\mathrm{does}\:\mathrm{the} \\ $$$$\mathrm{limit}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{d}\right)\:\mathrm{Is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{uniques}\:? \\ $$

Question Number 192543 Answers: 1 Comments: 0