What is the limit as z approaches 0 of z/(tan(z)) ?

The limit as z approaches 0 of z/(tan(z)) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as z approaches 0 of z/(tan(z))

z \to 0 lim (\frac{z}{tan ( z )})

1

Solution steps

z \to 0 lim (\frac{z}{tan ( z )})

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= z \to 0 lim (z cot (z))

Rewrite for L'Hopital

= z \to 0 lim (\frac{z}{\frac{1}{c o t ( z )}})

Apply L'Hopital's Rule

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

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

Plug in the value

z = 0

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

Simplify

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

= 1

\frac{d}{d t} (2 t + 7)

\frac{d}{d x} (2 - \frac{x}{4})

\int_{1}^{2} \frac{4}{( x - 1 ) ^{\frac{1}{4}}} d x

\frac{d}{d x} (\frac{1}{( - x ^{2} + 3 x + 3 ) ^{4}})

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

What is the limit as z approaches 0 of z/(tan(z)) ?
The limit as z approaches 0 of z/(tan(z)) is 1