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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 1

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