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

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

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limit as x approaches 0 of (sec(x)-1)/x

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{sec ( 0 ) tan ( 0 )}{1}

Simplify

\frac{sec ( 0 ) tan ( 0 )}{1} : 0

= 0

\frac{d}{d x} (\frac{1}{4 x - 1})

\int \frac{sec ( 2 y ) tan ( 2 y )}{4 + sec ( 2 y )} d y

- 2 x^{4} + 7 x e^{3 x - 2}

\int_{1}^{\infty} ln (x) d x

\frac{\partial}{\partial x} (\frac{t x ( 1 - x )}{1 - t ^{2}})

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