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

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

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/(tan(x))

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

1

Solution steps

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

Use the basic trigonometric identity:

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

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 1

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0

\int cos^{2} (x) sin^{2} (x) d x

(2 y^{2} + 3 x y) + (2 x y + x^{2}) y^{^{'}} = 0

x^{^{''}} + 9 x = 0, x (0) = 0.7, x^{^{'}} (0) = 0.4

x \to 2 lim (- x^{2})

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