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# mid2 - 5 Problem 4[10 points Estimate tan(0 001 using a...

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Math 1271, Lec 020: Calculus I Fall 2010 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] Differentiate the function. (a) [5 points] f ( x ) = cos(sin(tan x )) (b) [5 points] f ( x ) = sin 2 (tan x · ln x ) 2
(c) [5 points] f ( x ) = (1 + x 2 ) tan x (d) [5 points] f ( x ) = radicalbig ( 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] cos( xy ) = x tan y (b) [5 points] ( x 2 + 1) y = ( y 2 + 1) x 4
Problem 3. [10 points] Two cars start moving from the same point. One travels north at 30 mi/h and the other travels east at 40 mi/h. At what rate is the distance between the cars increasing after one hour later?

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Unformatted text preview: 5 Problem 4. [10 points] Estimate tan(0 . 001) using a linear approximation. 6 Problem 5. [10 points] Find the absolute minimum and the absolute maximum of the following function: f ( x ) = x 3-6 x 2-15 x + 25 for 0 ≤ x ≤ 6. 7 Problem 6. [20 points] Let f ( x ) = x 3-3 x 2-9 x + 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 point(s). (c) [6 points] Using the in±ormation ±rom parts (a) and (b), sketch the graph o± f . 8 Problem 7. [10 points] Show that x > sin x for 0 < x < π/ 2. 9 Problem 8. [10 points] Find the limit. (a) [5 points] lim x → ln(1 + x ) tan x (b) [5 points] lim x →∞ x 1 x 10...
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mid2 - 5 Problem 4[10 points Estimate tan(0 001 using a...

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