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# exam2 - h are abstract functions of x(a y = e x 2 − xf(b...

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Exam 2 M170-003 Spring, 2008 Name: (1 pt.) Show all your work. 1. (10 pts.) This problem requires that you compute a derivative using only secant slope and limits. You may assume the following facts: lim h 0 sin h h = 1 lim h 0 cos h - 1 h = 0 sin( a + b ) = sin a cos b + cos a sin b Compute the derivative of sin x at the location x = π/ 4. 1

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2. (35 pts.) For this and the remainder of the test you may use any methods. You must still show all your work. Find dy dx for each of the following: (a) y = 3 x 5 - x 2 + 14 x (b) y = sin 2 (3 x + 1) (c) y = cos(3 x 2 + 1) (d) y = cot x sec x 3 2
3. (20 pts.) Find y for each of the following, in which f , g

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Unformatted text preview: h are abstract functions of x . (a) y = e ( x 2 − xf ) (b) y = fg + h tan x 3 4. (10 pts.) Use the table of values at right to compute y ′ at x = 3 for y = f ( x 2 + g ( x )-5) x f g f ′ g ′ 2-1 4 7-6 3-2 5-4 5. (10 pts.) Suppose that csc y = x . Find dy/dx at the point where x = 2 and y = π/ 6. 4 6. (15 pts.) Two cars approach an intersection as shown at right. How fast is θ changing when the cars are both 50 feet from the intersection? car 1 30 mph car 2 20 mph θ 5...
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exam2 - h are abstract functions of x(a y = e x 2 − xf(b...

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