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LimitsQuestion and Answers: Page 4

Question Number 208093 Answers: 1 Comments: 0

lim_(n→∞) (1/n)((a+(1/n))^2 +(a+(2/n))^2 +...+(a+((n−1)/n))^2 )

$\lim_{n \to \infty} \frac{1}{n} ({(a + \frac{1}{n})}^{2} + {(a + \frac{2}{n})}^{2} + . . . + {(a + \frac{n - 1}{n})}^{2})$

Question Number 207816 Answers: 1 Comments: 1

lim_(x→2) ((((x^2 +4))^(1/3) −(√(x^3 −4)))/( (√(x^2 −4))−((x−2))^(1/3) ))

$\lim_{x \to 2} \frac{\sqrt[3]{x^{2} + 4} - \sqrt{x^{3} - 4}}{\sqrt{x^{2} - 4} - \sqrt[3]{x - 2}}$

Question Number 207528 Answers: 2 Comments: 0

Question Number 207339 Answers: 2 Comments: 0

lim_(x→∞) (((x+a)^(1/x) −x^(1/x) )/((x+b)^(1/x) −x^(1/x) )) =?

$\lim_{x \to \infty} \frac{{(x + a)}^{1 / x} - x^{1 / x}}{{(x + b)}^{1 / x} - x^{1 / x}} = ?$

Question Number 206992 Answers: 1 Comments: 0

Question Number 206934 Answers: 0 Comments: 3

Question Number 206730 Answers: 1 Comments: 1

find lim_(n→+∞) ∫_0 ^n e^(nx) arctan((x/n))dx

$f i n d {l i m}_{n \to + \infty} \int_{0}^{n} e^{n x} a r c t a n (\frac{x}{n}) d x$

Question Number 206702 Answers: 2 Comments: 0

lim_(n→∞) (√(cosn+sinn−3^n +4^n ))

$\lim_{n \to \infty} \sqrt{\cos n + \sin n - 3^{n} + 4^{n}}$

Question Number 206433 Answers: 2 Comments: 0

let f:[0,∞)→R be a continuous function if lim_(n→∞ ) ∫_0 ^1 f(x+n)dx = 2 then lim_(n→∞) f(nx) = ?

$let f : [0, \infty) \to R be a continuous function if$ $\lim_{n \to \infty} \int_{0}^{1} f (x + n) dx = 2$ $then \lim_{n \to \infty} f (nx) = ?$

Question Number 206095 Answers: 2 Comments: 0

Question Number 206069 Answers: 1 Comments: 0

lim_(x→0) ((−x^3 +x)/(sin x))

$\lim_{x \to 0} \frac{- x^{3} + x}{\sin x}$

Question Number 205916 Answers: 1 Comments: 0

lim_(x→0^+ ) xln(e^x −1)

${l i m}_{x \to 0^{+}} x l n (e^{x} - 1)$

Question Number 205774 Answers: 2 Comments: 0

−−−−−−− Ω = Σ_(n=0) ^∞ (( (−1)^( n) )/((−1)^( n) −n)) = ? −−−−−−−

$- - - - - - -$ $Ω = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{{(- 1)}^{n} - n} = ?$ $- - - - - - -$

Question Number 205727 Answers: 1 Comments: 4

calculate lim_(x→0) ((e^x −cosx)/x^2 )

$c a l c u l a t e {l i m}_{x \to 0} \frac{e^{x} - c o s x}{x^{2}}$

Question Number 205716 Answers: 2 Comments: 0

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

$\lim_{n \to \infty} \frac{(2 n + 1) (2 n + 3) . . . (4 n + 1)}{(2 n) (2 n + 2) . . . (4 n)} = ?$

Question Number 205580 Answers: 1 Comments: 2

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

$\lim_{n \to \infty} \frac{(2 n + 1) (2 n + 3) . . . (4 n + 1)}{(2 n) (2 n + 2) . . . (4 n)} = ?$

Question Number 205448 Answers: 0 Comments: 0

A=lim_(x→0) ((sinx)/x^3 )=?

$A = \lim_{x \to 0} \frac{s i n x}{x^{3}} = ?$

Question Number 205379 Answers: 2 Comments: 0

Question Number 205339 Answers: 1 Comments: 0

lim_(x→0) ((tan(tanx))/(sin(1−cosx)))

$\lim_{x \to 0} \frac{\tan (\tan x)}{\sin (1 - \cos x)}$

Question Number 205307 Answers: 1 Comments: 1

lim_(n→∞) ((⌊a⌋+⌊2a⌋+...+⌊na⌋)/n^2 ) where a∈R and ⌊x⌋ is the floor of x ∈ R

$\lim_{n \to \infty} \frac{⌊ a ⌋ + ⌊ 2 a ⌋ + . . . + ⌊ n a ⌋}{n^{2}} where a \in R$ $and ⌊ x ⌋ is the floor of x \in R$

Question Number 205237 Answers: 1 Comments: 0

Question Number 205142 Answers: 1 Comments: 0

lim_(n→∞) n^(−n^2 ) [(n+1)(n+(1/2))(n+(1/2^2 ))...(n+(1/2^(n−1) ))]^n =?

$\lim_{n \to \infty} n^{- n^{2}} {[(n + 1) (n + \frac{1}{2}) (n + \frac{1}{2^{2}}) . . . (n + \frac{1}{2^{n - 1}})]}^{n} = ?$

Question Number 205134 Answers: 1 Comments: 0

Question Number 205114 Answers: 1 Comments: 0

Solve: lim_((x,y)→(0,0)) ((1−cos((√(10xy))))/(3.y.sin(22x))) Ans.: (5/(66)) Step by step, please!

$S o l v e :$ ${l i m}_{(x, y) \to (0, 0)} \frac{1 - c o s (\sqrt{10 x y})}{3 . y . s i n (22 x)}$ $A n s . : \frac{5}{66}$ $S t e p b y s t e p, p l e a s e!$

Question Number 204991 Answers: 2 Comments: 1

Question Number 204929 Answers: 1 Comments: 0

lim_(n→∞) Π_(r=1) ^n ((n^2 −r)/(n^2 +r)) = ?

$\lim_{n \to \infty} \underset{r = 1}{\prod^{n}} \frac{n^{2} - r}{n^{2} + r} = ?$

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