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10BmidIver2s

# 10BmidIver2s - University of California San Diego...

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University of California, San Diego Mathematics Department MATH 10B Spring 2010 Midterm I Name Student ID TA Section This examination booklet contains 5 problems on 6 sheets of paper including the front cover. You have 50 minutes to answer all questions. You may use 8.5 by 11 inch ”cheat sheet”, front page only, hand written only. You may use a calculator. No books, notes, etc. are allowed. Work each problem in the space provided. If that space is insufficient, continue on the back of the page. Show your work. Answers without supporting work will be given little or no credit. Please do not write below this line. Points Total Question# Points 1 . / 10 2 . / 15 3 . / 10 4 . / 15 5 . / 20 Total Score /70

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1. A penguin is moving at velocity v ( t ) = 1 t +1 (m/h) for t = 0 to t = 2 hours. Use Δ t = 0 . 5 and the right hand sum to estimate the distance that the penguin travels during these 2 hours. Solution. L 4 = 1 2 1 1 / 2 + 1 + 1 1 + 1 + 1 3 / 2 + 1 + 1 2 + 1 = 1 2 2 3 + 1 2 + 2 5 + 1 3 = 1 2 · 57 30 = 57 60
2. Consider the graph of f ( x ) given below to answer (a), (b) and (c).

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