What is the limit as x approaches-pi/4+of-sec(2x) ?

The limit as x approaches-pi/4+of-sec(2x) is -infinity

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limit as x approaches-pi/4+of-sec(2x)

x \to - \frac{π}{4} + lim (- sec (2 x))

- \infty

Solution steps

x \to - \frac{π}{4} + lim (- sec (2 x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to - \frac{π}{4} + lim (sec (2 x))

Express with sin, cos

= - x \to - \frac{π}{4} + lim (\frac{1}{cos ( 2 x )})

For

x

approaching

- \frac{π}{4}

from the right

, x > - \frac{π}{4} \Rightarrow cos (2 x) > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \cdot \frac{d y}{d x} = y + x^{2} - y^{2}

x (x + 5 y) (\frac{d y}{d x}) + (y (3 x + 5 y)) = 0

\int (\frac{1}{sin ( x )}) d x

(x + 2)^{2} + (y - 3)^{2} = 37, (- 8, 2)

f (x) = x^{3} + 2 x, at x = - 1

What is the limit as x approaches-pi/4+of-sec(2x) ?
The limit as x approaches-pi/4+of-sec(2x) is -infinity