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

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

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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

x \to 1 lim (sin (1))

x \to - \infty lim (6 (x))

x \to 0 lim (\frac{1}{x} ln (1 + 2 x))

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

x \to 12 lim (10 - 3 x)

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