Quiz 1 Solutions

Quiz 1 Solutions - 2(4 marks It can be shown that b a x 4...

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MATHEMATICS 101 Section 202 Quiz #1, January 16, 2008 Show all your work. Use back of page if necessary. Calculators are not allowed. Last Name: First Name: UBC Stud. No.: 1. (6 marks) a) (4 marks) By evaluating the limit of Riemann sums obtained by using n equal-length subintervals and x i = x i , evaluate 3 0 (2 x 2 ) dx . You may use the formula n i =1 i 2 = n ( n + 1)(2 n + 1) / 6. b) (2 marks) The answer in part a) is a negative number. Explain, using a sketch, why this is so.
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Unformatted text preview: 2. (4 marks) It can be shown that b a x 4 dx = ( b 5 − a 5 ) / 5, where a and b are any real numbers. You may use this fact in this problem, without proving it. a) (2 marks) Evaluate 1 (8 x 4 − 3) dx . b) (2 marks) Prove the inequality 2 1 √ 4 x 8 + 1 dx ≥ 62 / 5....
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