Unit 4: Contextual Applications of Differentiation

A conical tank (vertex down) has a height of [math] m and a radius of [math] m at the top. Water is pumped in at a rate of [math] m[math]/min. Let [math] be the height and [math] be the surface radius of water.

Consider [math].

A particle moves along the [math]-axis with velocity [math] for [math], starting at position [math].

Evaluate each limit using L'Hôpital's Rule or other techniques.

A spotlight on the ground shines on a wall 12 m away. A person 2 m tall walks away from the spotlight toward the wall at 1.5 m/s.

A rectangular box with a square base and no top is to be made from [math] cm[math] of cardboard.

A particle moves in the [math]-plane so that [math] and [math] for [math].

A car travels on a straight road. Its velocity [math] (in ft/s) is recorded at various times.

Air is pumped into a spherical balloon at [math] cm[math]/s. The surface of the balloon is coated with paint that has a thickness [math] cm, where [math] is the radius.

Consider [math].