What is the limit as x approaches+0 of (x^2)/(1-cos(x)) ?

The limit as x approaches+0 of (x^2)/(1-cos(x)) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches+0 of (x^2)/(1-cos(x))

x \to + 0 lim (\frac{x ^{2}}{1 - cos ( x )})

2

Solution steps

x \to 0 lim (\frac{x ^{2}}{1 - cos ( x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 x}{sin ( x )})

= x \to 0 lim (\frac{2 x}{sin ( x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2}{cos ( x )})

= x \to 0 lim (\frac{2}{cos ( x )})

Plug in the value

x = 0

= \frac{2}{cos ( 0 )}

Simplify

\frac{2}{cos ( 0 )} : 2

= 2

\frac{d y}{d x} = \frac{5 x}{7 y}

\int \frac{1}{2} x cos (4 x^{2}) d x

\int - 2 x + 6 x^{2} - 4 x^{3} + C d x

\frac{\partial}{\partial y} (ln (1 + x y))

n = 1 \sum \infty \frac{1}{n} - \frac{1}{2 n + 1}

What is the limit as x approaches+0 of (x^2)/(1-cos(x)) ?
The limit as x approaches+0 of (x^2)/(1-cos(x)) is 2