Exercises

Answer each question.

1. What is the area of a circle with a radius of 17/4?

   area = 3.1415927*(17/4)²

   area = 56.745

2. What is the slope of the curve x³-3x²-10x+3 when x equals 2?

   Take the derivative to find an expression for the slope and evaluate at x=2.

   The derivative is 3x²-6x-10

   The slope at x=2 is -10

3. What is the area under the curve x³-3x²-10x+3 from x=-2.1905 to x=0.2788?

   The values -2.1905 and 0.2788 are approximations of two of the three points where the curve crosses the x-axis. They can be found by solving the equation x³-3x²-10x+3=0 for x.

   To find the area under the curve, compute the definite integral from the lower bound to the upper bound.

   The answer is 14.724

4. What is the surface area of a cylinder with radius 3 and height 5?

   The surface area of an entire cylinder can be computed by computing the surface area of the top (a circle), the bottom (a circle), and the side (a rectangle).

   The surface area of this cylinder is 150.7964

5. What is the ?