Math 201 Second Midterm Exam October 2008, Exams of Calculus

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Math 201

21 October 2008 Second Midterm

NAME (Print!): Check one: (1pm): (2pm):

Problem Points Score

1 20 2 20

3 10

4 30

5 20

Total 100

Problem 1 (20 points): The heat capacity C(T ) of a substance is the amount of energy (in joules) required to raise the temperature of 1 gram by 1 degree Celsius above temperature T. (a) Explain why the energy required to raise the temperature from T 1 to T 2 is the area under the graph of C(T ) over [T 1 , T 2 ]. (b) How much energy is required to raise the temperature from 50 to 100 degrees Celsius if C(T ) = 6 + 0. 2

T.

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NAME (Print!): Check one: (1pm): (2pm): Problem 3 (10 points): Let f (x) = 2x + 7 on [3, 6]. Find a formula for RN and find the area under f (x) by taking the limit.

Problem 5 (20 points): Let f (x) = x^2 − 5 x−6 and F (x) =

∫ (^) x 0 f^ (t)^ dt. (a) Find the critical points of F (x) and determine whether they are local minima or maxima. (b) Find the points of inflection of F (x) and determine whether the concavity changes from up to down or vice versa.

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