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

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?

Determine whether the series is convergent or divergent using the indicated test. State and check the conditions of the test before applying it. a. Integral Test

Within the eye, blood vessels would be found within sclera.