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McCartin_Test_3_Summer_2000 - MATH 101 TEST#3 Professor...

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Unformatted text preview: MATH 101 TEST #3 Professor Brian J. McCertt'n September 15,. 2000* 1. [2i] pts.) Boyle’s Law states that when a gas is compressed at a con. stant temperature, the pressure P and the volume V satisfy the equa- tion PV = (3', where C is a constant. Suppose that at a certain instant the volume is EDD cma, the pressure is 15!] lcPo, and the pressure is increasing at a rate of Eli chfmt‘n. At what rate is the volume rte- crcosing at this instant? 2. (10 pts.) Find the linearisstion Mrs) of HI} = e";I at o = fl. 3. (1D pts.) Find the diflerential tip of y = coax and evaluate tip for I :1: = sffi, dc = {1.135. 4. {2!} pts.) Find the points on the hyperbola y“ — 3:2 = 4 that are closest to the point {2.3:}. _ ’ "" “r e. {1e pts.) Using the Mean value Theorem, show that 1 v1+sc1+§cifztnfl e. [15 pte.) Ueitg l’H-fipital’s Rule, find e" — 1 lim :r—i-IJI sing: I T. [15 pts.) For f[$} = we”: _ c Find the intervals on which 3" is increasing or decreasing. c Find the local maximum and minimum values of f. c Find the intervals of concavityF and the inflection points. “WARNING: SHOW ALL WORK! ...
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