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Key points of this exam paper are: Package, Derivative, Each, Package, Length and Girth, Dimension, Box of Maximum, Volume, Square, Velocity
Typology: Exams
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FINAL EXAM - DECEMBER 15, 2004
Instruction: Read each question carefully. Explain ALL your work and give reasons to support your answers. Advice: DON’T spend too much time on a single problem.
Problems Maximum Score Your Score
1
2 FINAL EXAM - DECEMBER 15, 2004
(6 pts.)(b) f (x) = ln(x + 3x)
(6 pts.)(c) f (x) = 5
x + tan x
4 FINAL EXAM - DECEMBER 15, 2004
3.(15 pts.) Consider a sports car which accelerates from 0 ft/sec to 88 ft/sec in 5 seconds (88 ft/sec = 60 mph). The car’s velocity is given in the table below. t 0 1 2 3 4 5 v(t) 0 30 52 68 80 88 (8 pts.)(a) Using Riemann sums, find upper and lower bounds for the distance the car travels in 5 seconds.
(5 pts.)(b) Use your results in (a) to estimate
0 v(t)^ dt.
(4 pts.)(c) Estimate the average velocity of the car over the five second time interval.
MATH105A CALCULUS I - PROF. P. WONG 5
G(x)
H(x)
(4 pts.)(a) F (1)
(4 pts.)(b) F ′(1)
(4 pts.)(c) F (3)
(4 pts.)(d) F ′(3).
MATH105A CALCULUS I - PROF. P. WONG 7
(6 pts.)(b) Evaluate the following limit.
xlim→ 1 sin(ln(x
[x − cos(x − 1)].
(6 pts.)(c) Find the indefinite integral ∫ (
x − sin x) dx.
8 FINAL EXAM - DECEMBER 15, 2004
f’(x)
(6 pts.)(a) For what values of x does f have a local maximum or mini- mum? Explain.
(6 pts.)(b) For what values of x does f have an inflection point? Explain.
(6 pts.)(c) For what intervals is f increasing and for what intervals is f decreasing? Explain.
