mid2_practice

mid2_practice - 30 ft from the pole 5 Problem 4[10 points...

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Math 1271, Lec 020: Calculus I Fall 2010 (Practice) Midterm Exam II Instructions Check that this booklet consists of 10 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don’t need to simplify your answer. Good luck! Section and TA: Student ID: Name: Signature: Problems P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 Total Scores 1

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Problem 1. [20 points] Diferentiate the Function. (a) [5 points] f ( x ) = r 1 + R 1 + x (b) [5 points] f ( x ) = tan - 1 (ln(sin x )) 2
(c) [5 points] f ( x ) = (cos x ) cos x (d) [5 points] f ( x ) = ( x + 1)( x + 2) 2 ( x + 3) 3 ( x + 4) 4 ( x + 5) 5 ( x + 6) 6 3

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Problem 2. [10 points] Find dy/dx . (a) [5 points] x 3 y 3 = x + y + 1 (b) [5 points] (cos x ) y = (cos y ) x 4
Problem 3. [10 points] A street light is mounted at the top of a 20-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. At what rate is the lengh of his shadow increasing when he is

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Unformatted text preview: 30 ft from the pole? 5 Problem 4. [10 points] Estimate 4 √ 16 . 001 using a linear approximation. 6 Problem 5. [10 points] Find the absolute minimum and the absolute maximum of the following function: x √ 18-x 2 for-2 ≤ x ≤ 4. 7 Problem 6. [20 points] Let f ( x ) = x 4-4 x 3-6 . (a) [7 points] Find where f is increasing and where f is decreasing. (b) [7 points] Find where f is concave upward and where f is concave downward. Find the infection points. (c) [6 points] Using the in±ormation ±rom parts (a) and (b), sketch the graph o± f . 8 Problem 7. [10 points] Show that tan x > x for 0 < x < π/ 2. 9 Problem 8. [10 points] Find the limit. (a) [5 points] lim x → 2 e x-e 2 x 2-4 (b) [5 points] lim x → + x ln(sin x ) 10...
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mid2_practice - 30 ft from the pole 5 Problem 4[10 points...

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