What is the limit as x approaches 0+of x/(cos(4x)-1) ?

The limit as x approaches 0+of x/(cos(4x)-1) is -infinity

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limit as x approaches 0+of x/(cos(4x)-1)

x \to 0 + lim (\frac{x}{cos ( 4 x ) - 1})

- \infty

Solution steps

x \to 0 + lim (\frac{x}{cos ( 4 x ) - 1})

Apply L'Hopital's Rule

= x \to 0 + lim (\frac{1}{- 4 sin ( 4 x )})

For

x

approaching

0

from the right

, x > 0 \Rightarrow - 4 sin (4 x) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

What is the limit as x approaches 0+of x/(cos(4x)-1) ?
The limit as x approaches 0+of x/(cos(4x)-1) is -infinity