Evaluate the first derivative of the function below at (1, -2).

Evaluate the trigonometric function below from x = 2 up to x = 3.

The associated angles are in radians.

A ladder is 25 feet long and leaning against a vertical wall. The bottom of the ladder is pulled horizontally away from the wall at 3 feet per second. Determine how fast (in feet per second) the top of the ladder is sliding down the wall when the bottom is 15 feet from the wall.

An airplane is flying west at 500 ft/s at an altitude of 4000 ft and a searchlight on the ground lies directly under the path of the plane. If the light is kept on the plane, how fast is the searchlight revolving when the airline distance of the plane from the searchlight is 2000 ft due east?

What is the definite integral of:

Evaluate the polynomial function below from x = 2 up to x = 3.

Evaluate the function below from x = 2 up to x = 4.

All associated angles are in radians.

Evaluate the radical function below from x = 1 up to x = 5.

Evaluate the exponential function below from x = 1 up to x = 5.

Evaluate the trigonometric function below from x = 1 up to x = 5.

The associated angles are in radians.