Math 9B

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An Introduction to Mathematical Induction:
The Sum of the First n Natural Numbers,
Squares and Cubes.
Brief examples of proof by induction, with three formulas useful for evaluating Riemann sums.
Riemann Sums Finding the area under the curve as a limit.
U-substitution Some practice problems using u-substitution.
Integration by Parts Some practice problems using integration by parts.
Volume of a Sphere A proof of the formula for the volume of a sphere using volumes of revolution.

Sample Exams

Sample Midterm 1

Sample Midterm 2

Sample Midterm 3

Sample Final 1

Sample Final 2

Sample Final 3