MATH 205 Practice Final Exam Name: This test is closed-book and ...
MATH 205 Practice Final Exam Name: This test is closed-book and ...
MATH 205 Practice Final Exam Name: This test is closed-book and ...
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<strong>MATH</strong> <strong>205</strong><br />
<strong>Practice</strong> <strong>Final</strong> <strong>Exam</strong><br />
7. (16 points) A thirteen-foot-long ladder <strong>is</strong> leaning against a wall. The bottom of the ladder,<br />
which <strong>is</strong> currently five feet away from the wall, <strong>is</strong> slipping away from the wall at a rate of two<br />
feet per hour.<br />
(a) (8 points) How quickly <strong>is</strong> the top of the ladder sliding down the wall?<br />
(b) (8 points) How quickly <strong>is</strong> the angle between the ladder <strong>and</strong> the ground changing?<br />
8. (18 points) Evaluate the following integrals:<br />
(a) (6 points) ∫ 1<br />
θ sec2 (ln θ)dθ.<br />
(b) (6 points) ∫ 1<br />
0 x3 sin(x 4 + 2)dx<br />
(c) (6 points) ∫ 27<br />
1<br />
3√<br />
tdt<br />
Page 4 of 5 April 16, 2013
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