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Question Number 192606 Answers: 0 Comments: 1

proof that 0^0 =1 without limit!

$p r o o f t h a t 0^{0} = 1 w i t h o u t l i m i t!$

Question Number 192604 Answers: 0 Comments: 1

many people say that the 0^(0 ) is an uninfinity ones of them say that 0^0 is infinity and equal to 1! what do you think wich ones of them say right?

$m a n y p e o p l e s a y t h a t t h e 0^{0} i s a n u n i n f i n i t y$ $o n e s o f t h e m s a y t h a t 0^{0} i s i n f i n i t y a n d e q u a l t o 1!$ $w h a t d o y o u t h i n k w i c h o n e s o f t h e m$ $s a y r i g h t ?$

Question Number 192597 Answers: 1 Comments: 0

a_(1 ) , a_2 , a_(3 ) , .... , a_n is a sequence satifies that a_(n+2) =a_(n+1) −a_n for n ≥ 1. suppose the sum of the first 999 terms = 1003 and the sum of the first 1003 terms = −999 find the sum of the first 2002 terms.

$a_{1}, a_{2}, a_{3}, . . . ., a_{n} i s a s e q u e n c e s a t i f i e s t h a t$ $a_{n + 2} = a_{n + 1} - a_{n} f o r n \geq 1 . s u p p o s e t h e s u m$ $o f t h e f i r s t 999 t e r m s = 1003 a n d t h e s u m$ $o f t h e f i r s t 1003 t e r m s = - 999 f i n d t h e$ $s u m o f t h e f i r s t 2002 t e r m s .$

Question Number 192596 Answers: 2 Comments: 0

Question Number 192594 Answers: 0 Comments: 0

Question Number 192593 Answers: 0 Comments: 0

Question Number 192590 Answers: 1 Comments: 0

Σ_(n=1) ^∞ Σ_(m=1) ^∞ [((m^2 n)/(3^m (3^n .m+3^m .n)))]=λ find λ.

$\underset{n = 1}{\sum^{\infty}} \underset{m = 1}{\sum^{\infty}} [\frac{m^{2} n}{3^{m} (3^{n} . m + 3^{m} . n)}] = λ$ $f i n d λ .$

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))

$This might be helpful :$ $How to easily calculate z_{1}^{z_{2}} with z_{1}, z_{2} \in C :$ $Transform z_{1} = r e^{i θ} and z_{2} = a + b i \Rightarrow$ $z_{1}^{z_{2}} = {(r e^{i θ})}^{a + b i}$ $z_{1}^{z_{2}} = r^{a + b i} e^{- b θ + i a θ}$ $z_{1}^{z_{2}} = r^{a} e^{- b θ} r^{b i} e^{i a θ}$ $z_{1}^{z_{2}} = \frac{r^{a}}{e^{b θ}} e^{i (a θ + b \ln r)}$

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.

$Let A B C D be a rectangle having an area of 290 .$ $Let E be on B C such that B E : B C = 3 : 2 .$ $Let F be on C D such that C F : F D = 3 : 1 .$ $If G is the intersection of A E and B F, compute$ $the area of △ B E G .$

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

$s o l v e;$ $\lim_{x \to 0} x^{2} t a n (\frac{s i n π x}{2 x})$ $s o l u t i o n$ $l e t L = \lim_{x \to 0} x^{2} t a n (\frac{s i n π x}{2 x})$ $s i n c e s i n x \sim x - \frac{x^{3}}{6}$ $L = \lim_{x \to 0} x^{2} t a n (\frac{π x}{2 x} - \frac{π^{3} x^{3}}{12 x})$ $L = \lim_{x \to 0} x^{2} t a n (\frac{π}{2} - \frac{π^{3} x^{2}}{12})$ $s i n c e t a n (\frac{π}{2} - x) = \frac{1}{t a n x}$ $L = \lim_{x \to 0} \frac{x^{2}}{t a n (\frac{π^{3} x^{2}}{12})}$ $L = \lim_{x \to 0} \frac{\frac{π^{3} x^{2}}{12}}{t a n (\frac{π^{3} x^{2}}{12})} \frac{12}{π^{3}}$ $L = \frac{12}{π^{3}} \lim_{x \to 0} \frac{\frac{π^{3} x^{2}}{12}}{t a n (\frac{π^{3} x^{2}}{12})}$ $s i n c e \lim_{x \to 0} \frac{x}{t a n x} = 1$ $L = \frac{12}{π^{3}} \cdot 1 = \frac{12}{π^{3}}$ $s o l v e d b y H Y a . k . a s e n e s t r o$

Question Number 192550 Answers: 1 Comments: 0

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

$h o w c a n f i n d t h e s u m \underset{i = 1}{\sum^{r}} (2 v_{i} + 1) ?$

Question Number 192549 Answers: 2 Comments: 0

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

$\lim_{x \to 0} x^{2} \tan (\frac{\sin π x}{2 x}) = ?$

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 ?

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