241ex1f - Calculus I (Math 241) Test 1 (No Work No Credit)...

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Calculus I (Math 241) – Test 1 (No Work – No Credit) Problem 1. [10 Points] Let v = ( 1 4 ) and w = ( 2 1 ). Find v + w , || v || , the unit vector in the direction of w , v · w , and the cosine of the angle enclosed by v and w . Problem 2. [10 Points] Find an interval of length at most 1 / 2 and prove that the equation x 5 - x 2 + 2 x + 3 = 0 has a root in it. Problem 3. [10 Points] Calculate the following limits. If there is no limit, say so. (1) lim t 2 t 2 + t - 6 t 2 - 4 and (2) lim x 0 x 1 + 3 x - 1 . Problem 4. [10 Points] Di±erentiate f ( x ) = x 3 - 2 using ²rst principles. No credit for just writing down the derivative. Problem 5. [10 Points] Use approximation by di±erentials to ²nd an ap-
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This note was uploaded on 07/26/2009 for the course MATH 215 taught by Professor Heiner during the Spring '09 term at Hawaii.

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