finalreview

# finalreview - written, concise and logical answer.) 3...

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Math 21A - Final Review Question 1 (20 points) Supertankers off-load oil at a docking facility 2 miles offshore. The reﬁnery is 2 miles down the coast from the point on the shore nearest the docking facility. A pipeline must be constructed connecting the docking facility with the reﬁnery. The pipeline costs \$ 2,000,000 per mile if constructed underwater and \$ 1,000,000 per mile if on land. Find the minimum cost of constructing the pipeline. 1

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Question 2 (20 points) (i) Write out in words what the following mathematical symbols mean and then give a precise deﬁnition: lim x →∞ f ( x ) = L . (ii) Use your deﬁnition in (i) to prove lim x →∞ x 2 - 2 x + 2 x 2 - 2 x + 1 = 1 . 2
Question 3 (20 points) Fill in the blanks d log x 2 dx = d 2 log x 2 dx 2 = d 3 log x 2 dx 3 = d n log x 2 dx n = Explain (but do not prove) why your last answer is correct. (Full points for a well

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Unformatted text preview: written, concise and logical answer.) 3 Question 4 (20 points) Find the derivative of: y = sin ( 2 x + 5 x 3 ) Find d dx p 1 + tan ( f ( x )) = Find d 2 dx 2 5 √ 1-x 3 = Find g ( t ) if g ( t ) = e 9 t sin 5 2 t 4 Question 5 (20 points) Below is the graph of the velicity, in feet per second, of a partical at time t seconds. Using the graph of the velocity above plot the acceleration of the partical at time t . Given that the partical starts at zero at t = 0 and ten seconds later is at a position three feet below the origin, that is p (0) = 0 and p (10) =-3 . Graph the position of the partical verses time below. 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.

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finalreview - written, concise and logical answer.) 3...

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