Find an equation of the tangent to the curve at the given point without eliminating the parameter.

BONUS question The movement of a bone around its long axis or vertical axis is called

BONUS question What are the pigments responsible for skin color ?

Find the exact area of the surface obtained by rotating the curve about the x-axis. No approximations. Do not use banned calculators. Show all steps for full credit.

Find the solution of the differential equation that satisfies the given initial condition.

Evaluate the integrals. No approximations – use fractions to state the final answer. Do not use banned calculators. a.

Use the Trapezoidal, Midpoint OR Simpson’s Rule with 4 subintervals to approximate the integral – round to 6 decimal places.

BONUS question The articulation of the head of the humerus in the glenoid cavity of the scapula is an example of a:

Find the average value of the function on the given interval. Show all steps and do not use banned calculators for full credit. Use 3 decimal places.

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?