GCSU Calculus & Mathematics Practice Quiz

Problem 1:

A spring hanging vertically is stretched and its height, in inches, above ground after ??seconds is given by ?(?)=50?8cos(??6)?(?)=50?8cos(??6). Round all numerical answers to the nearest tenth and give correct units where appropriate.

How high is the spring after 4 seconds?

What is the spring’s velocity after 4 seconds?

What is the spring’s acceleration after 4 seconds?

Is the spring moving up or down at ?=4?=4 seconds? Briefly justify your conclusion.

Is the spring speeding up or slowing down at ?=4?=4 seconds? Briefly justify your conclusion.

Problem 2:

Approximate the value of sin(31?)sin(31?)using linear approximation. [Hint: Convert 31?31? to radians]. Round your answer to 5 decimal places. For this problem, you may use a calculator approximation of ??, but you cannot use a calculator approximation for sin(31?)sin(31?).