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LimitsQuestion and Answers: Page 1

Question Number 219223 Answers: 1 Comments: 0

Question Number 218703 Answers: 3 Comments: 0

Prove; lim_(x→0) ((x − sin x)/x^3 ) = (1/6)

$P r o v e; {l i m}_{x \to 0} \frac{x - s i n x}{x^{3}} = \frac{1}{6}$

Question Number 218543 Answers: 1 Comments: 1

Question Number 218196 Answers: 3 Comments: 0

lim _(n→∞) (1/n) ( (((2n)!)/(n!)) )^(1/n) = ?

$\lim_{n \to \infty} \frac{1}{n} {(\frac{(2 n)!}{n!})}^{\frac{1}{n}} = ?$

Question Number 217190 Answers: 1 Comments: 0

Given a_(n+1) = a_n + a_(n+2) where a_3 = 4 and a_5 = 6 find a_n .

$Given a_{n + 1} = a_{n} + a_{n + 2}$ $where a_{3} = 4 and a_{5} = 6$ $find a_{n} .$

Question Number 216952 Answers: 0 Comments: 0

Question Number 216953 Answers: 0 Comments: 1

Question Number 216926 Answers: 1 Comments: 0

Evaluate 5^2 Σ_(n=1) ^∞ (1/2)(Σ_(m=2) ^∞ (2/(m^2 +2m)))^(n−1)

$E v a l u a t e 5^{2} \underset{n = 1}{\sum^{\infty}} \frac{1}{2} {(\underset{m = 2}{\sum^{\infty}} \frac{2}{m^{2} + 2 m})}^{n - 1}$

Question Number 216925 Answers: 1 Comments: 0

Question Number 216917 Answers: 1 Comments: 0

lim_(x→+∞) ((√(x+(√(x+(√(x+(√x)))))))−(√x))

$l i \underset{x \to + \infty}{m} (\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x}}}} - \sqrt{x})$

Question Number 216748 Answers: 1 Comments: 0

Find ∫_(−1) ^1 ln∣Γ((1/2)+it)∣dt

$F i n d \int_{- 1}^{1} l n ∣ Γ (\frac{1}{2} + i t) ∣ d t$

Question Number 216274 Answers: 0 Comments: 0

prove that : Σ_(n=1) ^∞ (( cos( n ))/n) ( 1+(1/( (√2))) + (1/( (√3))) + ...+(1/( (√n))) ) is convergent.

$p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} \frac{c o s (n)}{n} (1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + . . . + \frac{1}{\sqrt{n}})$ $i s c o n v e r g e n t .$

Question Number 216055 Answers: 1 Comments: 0

lim_(x→0) ((sin^2 2x)/( ((cos x))^(1/3) −((cos x))^(1/4) )) =?

$\lim_{x \to 0} \frac{\sin^{2} 2 x}{\sqrt[3]{\cos x} - \sqrt[4]{\cos x}} = ?$

Question Number 216032 Answers: 2 Comments: 0

lim_(x→0) ((1−cos x (√(cos 2x)))/x^2 ) =?

$\lim_{x \to 0} \frac{1 - \cos x \sqrt{\cos 2 x}}{x^{2}} = ?$

Question Number 216014 Answers: 1 Comments: 0

lim_(Δx→cos(π/2)) ((sin^3 (Δx+x)−sin^3 x)/(2^(−1) ∙Δx))=?

$\lim_{Δ x \to c o s \frac{π}{2}} \frac{\sin^{3} (Δ x + x) - {s i n}^{3} x}{2^{- 1} \cdot Δ x} = ?$

Question Number 215884 Answers: 1 Comments: 0

lim_(x→0) ((cos 2x−cos 6x)/(1−cos 3x cos 5x)) =?

$\lim_{x \to 0} \frac{\cos 2 x - \cos 6 x}{1 - \cos 3 x \cos 5 x} = ?$

Question Number 215831 Answers: 2 Comments: 0

lim_(x→∞) (((√((x+1)^3 ))−(√((x−1)^3 )))/( (√x))) =?

$\lim_{x \to \infty} \frac{\sqrt{{(x + 1)}^{3}} - \sqrt{{(x - 1)}^{3}}}{\sqrt{x}} = ?$

Question Number 215779 Answers: 0 Comments: 5

Question Number 215748 Answers: 1 Comments: 0

lim_(n→∞) [Π_(k=1) ^(n+1) Γ((1/k))]^(1/(n+1)) −[Π_(k=1) ^n Γ((1/k))]^(1/n)

$\lim_{n \to \infty} {[\underset{k = 1}{\prod^{n + 1}} Γ (\frac{1}{k})]}^{\frac{1}{n + 1}} - {[\underset{k = 1}{\prod^{n}} Γ (\frac{1}{k})]}^{\frac{1}{n}}$

Question Number 215739 Answers: 1 Comments: 0

Question Number 215718 Answers: 1 Comments: 0

lim_(x→∞) (ln(9/2))^((1/2)x) =?

$\lim_{x \to \infty} {(l n \frac{9}{2})}^{\frac{1}{2} x} = ?$

Question Number 215667 Answers: 2 Comments: 0

lim_(x→1) sec((π/2)x)(arctanx−(π/4))=?

$\lim_{x \to 1} s e c (\frac{π}{2} x) (a r c t a n x - \frac{π}{4}) = ?$

Question Number 215343 Answers: 1 Comments: 1

lim_(x→0) ((sin 3xcos5x )/x^2 )

$\lim_{x \to 0} \frac{\sin 3 x \cos 5 x}{x^{2}}$

Question Number 215808 Answers: 1 Comments: 0

⇃

$⇃ \underset{―}{}$

Question Number 215051 Answers: 1 Comments: 0

lim_(n→∞) Π_(k=1) ^n ((k^2 +1)/( (√(k^2 +4))))=?

$\lim_{n \to \infty} \underset{k = 1}{\prod^{n}} \frac{k^{2} + 1}{\sqrt{k^{2} + 4}} = ?$

Question Number 214900 Answers: 2 Comments: 0

determinant ()

Question Number 214712 Answers: 2 Comments: 0

$\underset{―}{\underset{⏟}{x}}$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

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