1. (25 Points) Find the limits of the following five (5) functions. Provide a sketch of the function validating your Answer.

2. (10 points) Explain the Sandwich Theorem and provide a sketch of two example functions "sandwiching" a third function. Include the equations of the functions!

3. (20 Points) Calculate the derivatives of the following four functions using limits and the difference quotient:

4. (25 points) A rocket's horizontal displacement (in meters) to a target as a function of time (in seconds) is given by the function:

Determine the time (in seconds after launch) the rocket's velocity will be 1000 meters/second.

Remember:

5. (20 points)

Calculate: The velocity of a frictionless ball falling from the Royal Gorge Bridge when it strikes the river 1031 feet below. Assume no initial velocity when dropped.