mid2sample2

# mid2sample2 - π 100 ² 5(6 points Two carts are connected...

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Math 1A, Spring 2008, Wilkening Another Sample Midterm 2 1. (1 point) write your name, section number, and GSI’s name on your exam and write your name on your sheet of notes. 2. (3 points) Suppose f is twice diﬀerentiable on the interval [0 , 4] and satisﬁes f 0 (0) = 1 f 00 (0) = - 1 f 0 (1) = 0 f 00 (1) = - 2 f 0 (2) = 0 f 00 (2) = 0 f 0 (3) = - 1 f 00 (3) = 1 f 0 (4) = 0 f 00 (4) = 1 At the endpoints x = 0 and x = 4, these are one-sided derivatives. Fill in the following table with YES, NO, or CBT (cannot be determined). c = 0 1 2 3 4 f has a local max at c f has a local min at c 3. (5 points) Let f ( x ) = x x . Compute f 0 (2), f 0 (4) and ( f f ) 0 (2). Note that 4 4 = 256. 4. (5 points) Use a linear approximation to estimate: 1 π tan - 1 ± 1 +
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Unformatted text preview: π 100 ² . 5. (6 points) Two carts are connected by a 35 foot rope that passes over a pulley 12 feet above the ﬂoor. Cart A is being pulled to the left at a speed of 2 ft/sec. How fast is cart B moving at the instant cart A is 9 feet from the point on the ﬂoor beneath the pulley? 20 cart A cart B pulley 12 9 15 16 6. (5 points) Show that there is exactly one x ∈ R satisfying x 5 + e x-2 = 0 . 7. (5 points) Do one of the following: (a) Show that tanh(sinh-1 x ) = x √ 1 + x 2 ( x ∈ R ) . (b) If g ( x ) = 1 + x + e x , ﬁnd g-1 (2) and ( g-1 ) (2)....
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## This note was uploaded on 09/24/2009 for the course MATH 1A taught by Professor Wilkening during the Spring '08 term at Berkeley.

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