What is the limit as θ approaches+0 of (tan(2θ))/θ ?

The limit as θ approaches+0 of (tan(2θ))/θ is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as θ approaches+0 of (tan(2θ))/θ

θ \to + 0 lim (\frac{tan ( 2 θ )}{θ})

2

Solution steps

θ \to 0 lim (\frac{tan ( 2 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{sec ^{2} ( 2 θ ) \cdot 2}{1})

= θ \to 0 lim (\frac{sec ^{2} ( 2 θ ) \cdot 2}{1})

Plug in the value

θ = 0

= \frac{sec ^{2} ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{sec ^{2} ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

x \to 3 + lim (\frac{x - 3}{x - 2 - 4 - x})

n = 1 \sum \infty i^{2 n}

n = 2 \sum \infty n (\frac{3}{4})^{n}

x \to 1 lim (\frac{x}{x - 1})

x \to 7 lim (x + 2 - 3)

What is the limit as θ approaches+0 of (tan(2θ))/θ ?
The limit as θ approaches+0 of (tan(2θ))/θ is 2