In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=\sin 2 x, \quad x=\frac{\pi}{4}$$

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=2 x^2+3, \quad x=-1$$

Find the curvature and radius of curvature of the plane curve at the given value of $x$.

$$y=\frac{3}{4} \sqrt{16-x^2}, \quad x=0$$

Find the curvature and radius of curvature of the plane curve at the given value of x. y = 3/4 √16-x², x= 0

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=e^{-x / 4}, \quad x=8$$

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=e^{-x / 2}, \quad x=0$$

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=2 x+\frac{4}{x}, \quad x=1$$

Find the curvature and radius of curvature of the plane curve at the given value of $x$.

$$y=\tan x, \quad x=\frac{\pi}{4}$$

find the curvature.

$$y = tan x$$

Calculate the curvature.

$$y=x^{3 / 2}$$

Find the curvature and radius of curvature of the plane curve at the given value of x. $y=5 x^{2}+7$, x=-1

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=2 \sqrt{9-x^2}, \quad x=0$$

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=5 x^2+7, \quad x=-1$$

In the following exercise, find the curvature and radius of curvature of the plane curve at the given value of x.

$$y=\frac{1}{2} x^2+x, \quad x=4$$