MTH 421 Midterm: Midterm 1 Spring 2009
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Instructions: no calculators, books, notes, or electronic devices may be used during the exam, you have 50 minutes, there are 4 problems, some with multiple parts. Complete all problems, and write all solutions in the space provided on the exam: unless indicated otherwise, you may use any theorem proved in the lecture, or any theorem from single variable di erential calculus. When applying a theorem, you should explicitly verify that all necessary hypotheses are met: additional scratch paper is provided at the end of the exam. Total (50 points: determine whether each of the following statements is true or false. If a statement is false, provide a counterexample. (write out the word true or false completely!) (a) let f , g : [a, b] r be integrable functions. Assume that f (x) g(x) for all x [a, b], a g(x) dx. and that there exists a point c [a, b] so that f (c) > g(c).
