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Unformatted text preview: Math 21A
1 (32 pts.) Brian Osserman Practice Exam 1 Determine whether or not the following limits exist, and calculate them. If the limit does not exist as a number, state whether or not it can be written as or .
x3 (a) limx3 x2 2x3 (b) limt0 t+11 t (c) limx1+ 2x2 1x (d) limx sin x 2 (8 pts.) Using the sandwich theorem, show that limx0 x4 (1  cos x) = 0. 3 (12 pts.) Directly from the denition of a limit, show that limx3 x2 = 9. 2 4 (16 pts.) Find limx 1cos(1/x) . (Hint: use the double angle formula) (1/2x) 3 5 (16 pts.) Graph the function
f (x) = x3 2x2 +2x4 2 : x = 1, 2 x 3x+2 4 : x = 1, 2 (Hint: factor the denominator rst) Find all asymptotes to the graph. At which points is this function continuous, and at which points is it discontinuous? For each discontinuity, say whether or not it is removable. 4 6 (8 pts.) Show that the equation x3  x  1 = 0 has a solution in the interval [1, 2]. 7 (8 pts.) At t seconds after lifto, the height of a rocket is 4t2 feet. How fast is the rocket climbing 10 seconds after lifto? (Compute this from our denitions, without using derivative laws) 5 ...
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This note was uploaded on 10/07/2008 for the course MATH 21A taught by Professor Osserman during the Spring '07 term at UC Davis.
 Spring '07
 Osserman
 Limits

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