MAT112 Calculus II Pretest #1
1. Use the data points to plot a linear regression:
2. After performing a quadratic regression, you obtain the formula y(x) = x(x-2). Find the area under the curve between 0 and 2 in the following manners:
a.) Estimate the area with 4 rectangles of equal width.
b.) Estimate the area with 4 rectangles using x1=.5, x2=1 x3=1.25 and x4=2 and Δx1=1, Δx2=.25, Δx3=.25, Δx4=.5 Draw a picture of this approximation.
c.) If and show how you might find the exact area as a limit as n goes to infinity of a sum of equally spaced rectangles of width 2/n
d.) Verify this by finding a definite integral.
e.) Check this value in the calculator
3. Evaluate the integrals:
4. Evaluate the integral using a geometric approach
5. Explain what is wrong with this integral.
6. Evaluate the integral using substitution.
What is the average value of over the interval [-2,3]?
7. If the acceleration a(t) = -10 and v0 = 30, find the velocity v(t).
What is the displacement from t = 0 to t = 4?
What is the distance traveled from t = 0 to t = 4?
8. Sketch the curve y = 1/t and shade the region under the curve whose area is ln3.
If ln a = 2, find a.
Give an integral whose area is 2.