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

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

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

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

- \infty

Solution steps

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

For

x

approaching

0

from the right

, x > 0 \Rightarrow cos (x) - 1 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

\int x^{2} \cdot sec^{2} (x^{3}) d x

x \to 0 lim (\frac{x ^{3} - 0}{x})

n = 1 \sum \infty n e^{- 3 n}

x \to \frac{π}{2} lim (\frac{1 - tan ( 2 x )}{2 tan ( x )})

x^{- 8 c o s (x)}

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