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

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

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

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

- \infty

Solution steps

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

Express with sin, cos

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

For

x

approaching

0

from the left

, x < 0 \Rightarrow x cos (x) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

y^{^{''}} + 6 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\frac{d}{d x} ((x - 1)^{2} + y^{2})

f (x) = x^{3} + 2 x

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

y = \frac{x - 4}{x}

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