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

x \to 1 - lim (x^{3} - 1)

x \to 5 + lim (\frac{x + 1}{x + 5})

x \to 0 - lim (ln (x^{2} - 4 x))

x \to 0 lim (\frac{sin ( 5 x ^{2} )}{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