Unformatted text preview: MATH 140 EXAM #2 MARCH 14, 2003
Dr. Ellis INSTRUCTIONS:
1. Write your name and TA’s name on every answer sheet. 2. Answer each problem on a separate answer sheet.
3. SHOW WORK AND GIVE REASONS. NO CALCULATORS. [24] 1. (a) Let ﬁx) = xi? Use the definition of the derivative as a limit to
find f ’(2). (b) Using the fact that cscx= sill” and the quotient rule, derive the formula for the derivative of cscx. [39] 2. In each of the following, find f’(x). (a) ﬁx) = x1/3e" + Slnx. (b) ﬁx) 2 2 sinx 3 cosx — 4tanx' (C) ﬂx) = xJ4 + scczx [12] 3. (a) Approximate tan(7r/4+0.2). [10] (b) Suppose we want to approximate a solution of x”i — x — 1 = 0
using the NewtonRaphson method with initial estimate equal to 1.
Find the next estimate given by the NewtonRaphson method.
Hint: c...1 = c. — M.
f (cn) [15] 4. A car is driving east away from a traffic light at the rate of 30 feet per
second. A police car is driving north towards the same light at the rate of
20 feet per second. How fast is the distance between the two cars changing
when the police car is 300 feet from the light and the other car is 400 feet
from the light? mrh:3/03
a: 1 40x2elisSp03 ...
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