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LimitsQuestion and Answers: Page 8

Question Number 196135 Answers: 0 Comments: 0

Question Number 196072 Answers: 2 Comments: 0

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Question Number 195982 Answers: 2 Comments: 0

lim_(x→1) [(1/(2(1−(√x))))−(1/(3(1−(x)^(1/3) )))]=? with out l′pital rule

$\lim_{x \to 1} [\frac{1}{2 (1 - \sqrt{x})} - \frac{1}{3 (1 - \sqrt[3]{x})}] = ?$ $w i t h o u t l^{'} p i t a l r u l e$

Question Number 195947 Answers: 2 Comments: 0

Question Number 195905 Answers: 1 Comments: 0

lim_(x→0) (((√(3+x^4 )) −(√(3+tan^4 x)))/x^6 ) =?

$\lim_{x \to 0} \frac{\sqrt{3 + x^{4}} - \sqrt{3 + \tan^{4} x}}{x^{6}} = ?$

Question Number 195840 Answers: 0 Comments: 4

find the valur lim_(→0) ((x−sinx)/x^3 )

$f i n d t h e v a l u r$ $l i \underset{\to 0}{m} \frac{x - s i n x}{x^{3}}$

Question Number 195772 Answers: 2 Comments: 0

$\underset{―}{\underset{⏟}{}}$

Question Number 195619 Answers: 2 Comments: 0

$\underset{―}{\underset{⏟}{}}$

Question Number 195618 Answers: 4 Comments: 0

$\underset{―}{\underset{⏟}{}}$

Question Number 195569 Answers: 0 Comments: 0

a_i ,b_i ,x_i be reals for i=1,2,3,...,n, such that Σ_(i=1) ^n [a_i x_i ]=0. Prove that (Σ_(i=1) ^n [x_i ^2 ])(Σ_(i=1) ^n [a_i ^2 ]Σ_(i=1) ^n [b_i ^2 ]−(Σ_(i=1) ^n [a_i b_i ])^2 )≥(Σ_(i=1) ^n [a_i ^2 ])(Σ_(i=1) ^n [b_i x_i ])^2

$a_{i}, b_{i}, x_{i} b e r e a l s f o r i = 1, 2, 3, . . ., n, s u c h t h a t$ $\sum_{i = 1}^{n} [a_{i} x_{i}] = 0 . P r o v e t h a t$ $(\underset{i = 1}{\sum^{n}} [x_{i}^{2}]) (\underset{i = 1}{\sum^{n}} [a_{i}^{2}] \underset{i = 1}{\sum^{n}} [b_{i}^{2}] - {(\underset{i = 1}{\sum^{n}} [a_{i} b_{i}])}^{2}) ⩾ (\underset{i = 1}{\sum^{n}} [a_{i}^{2}]) {(\underset{i = 1}{\sum^{n}} [b_{i} x_{i}])}^{2}$

Question Number 195401 Answers: 1 Comments: 0

calcu_⇓_⇓ late lim_( x→(π/2)) ( sin(x ))^( tan^( 2) (x )) = ? determinant ((),())

$calc \underset{\underset{⇓}{⇓}}{u l a t e}$ $\lim_{x \to \frac{π}{2}} {(\sin (x))}^{\tan^{2} (x)} = ? \begin{array}{cc} \end{array}$

Question Number 195365 Answers: 2 Comments: 0

_(x→y) ^(lim) ((tan x−tany)/(x−y))

$\underset{x \to y}{\overset{\lim}{}} \frac{\tan x - tany}{x - y}$

Question Number 195395 Answers: 1 Comments: 0

Question Number 195325 Answers: 2 Comments: 0

prove that lim_(x→(π/2)) ((tan((x/2))−1)/(x−(π/2)))=1

$p r o v e t h a t$ $\lim_{x \to \frac{π}{2}} \frac{t a n (\frac{x}{2}) - 1}{x - \frac{π}{2}} = 1$

Question Number 195315 Answers: 1 Comments: 0

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Question Number 200300 Answers: 1 Comments: 0

Question Number 200298 Answers: 1 Comments: 1

Question Number 195259 Answers: 0 Comments: 1

prove that lim_(n→∞) ((e^n ∙(n!))/(n^n (√n)))=(√(2π))

$p r o v e t h a t$ $\lim_{n \to \infty} \frac{e^{n} \cdot (n!)}{n^{n} \sqrt{n}} = \sqrt{2 π}$

Question Number 195231 Answers: 1 Comments: 0

determinant ((( )))

$\begin{matrix} \underset{―}{\underset{⏟}{}} \end{matrix}$

Question Number 195195 Answers: 1 Comments: 1

find the limit: _(x→a ) ^(lim) (x^(1/3) /x^(1/2) ) − (a^(1/3) /a^(1/2) )

$find the limit :$ $\underset{x \to a}{\overset{\lim}{}} \frac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}} - \frac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}$

Question Number 195154 Answers: 1 Comments: 0

lim_(x→2π) (((tan (π cos x))/(x^2 (x−5π)+4π^2 (2x−π))))=?

$\lim_{x \to 2 π} (\frac{\tan (π \cos x)}{x^{2} (x - 5 π) + 4 π^{2} (2 x - π)}) = ?$

Question Number 195148 Answers: 3 Comments: 0

determinant (((lim_(x→0) ((1+x sin x−cos x)/(sin^2 x))=?)))

$\begin{matrix} \lim_{x \to 0} \frac{1 + x \sin x - \cos x}{\sin^{2} x} = ? \end{matrix}$

Question Number 195136 Answers: 1 Comments: 0

f(x)=arctan(sinx) and cosa=(2/3) faind f^′ (a)=?

$f (x) = a r c t a n (s i n x)$ $a n d c o s a = \frac{2}{3} f a i n d f^{^{'}} (a) = ?$

Question Number 195093 Answers: 2 Comments: 0

Question Number 195075 Answers: 1 Comments: 0

lim_(x→∞) ((sin^2 x−cos^3 x)/x)

$\lim_{x \to \infty} \frac{{s i n}^{2} x - {c o s}^{3} x}{x}$

Question Number 195066 Answers: 0 Comments: 0

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