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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- sec ( x ) + 2 sec ^{3} ( x )}{1})

= x \to 0 lim (\frac{- sec ( x ) + 2 sec ^{3} ( x )}{1})

Plug in the value

x = 0

= \frac{- sec ( 0 ) + 2 sec ^{3} ( 0 )}{1}

Simplify

\frac{- sec ( 0 ) + 2 sec ^{3} ( 0 )}{1} : 1

= 1

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