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408CF09assign2

# 408CF09assign2 - at each point of discontinuity to justify...

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M408C Fall 2009 Assignment 2 Due Thursday, September 10 You should have read and understood sections 2.5, 3.1, and 3.2 before completing this assignment. You must show suﬃcient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. You may use calculators for arithmetic. I strongly discourage you from using a cal- culator to do any algebraic simpliﬁcations, etc., since you will not be allowed to use one on the exams. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. Find all points where the function f given below is discontinuous. Classify each discontinuity as a removable discontinuity, jump discontinuity, or neither. Take limits
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Unformatted text preview: at each point of discontinuity to justify your conclusions. f ( x ) = x 2-4 x + 4 | x 2-3 x + 2 | , x ≥ sin x, x < 2. Use the deﬁnition of derivative to calculate f ( x ) for f ( x ) = √ 2 x + 5. 3. Show that the graph of the function f ( x ) = 2 cos x-x 2 crosses the x axis. Approximate the x-intercept with one decimal place accuracy. (In other words, the diﬀerence between your approximation and the actual intercept must be less than 0.05). 4. Let g ( x ) = x 2 5 . (a) Is g continuous at x = 0? Use the deﬁnition of continuity to justify your answer. (b) Is g diﬀerentiable at x = 0? Use the deﬁnition of diﬀerentiablity to justify your answer. 5. Let f ( x ) = x 1 3 ± 1 + cos ± 1 x ¶¶ . Does lim x → f ( x ) exist? Is f continuous at x = 0? Is f diﬀerentiable at 0? Justify your answers....
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