Workshop #27 | University of North Dakota - Edubirdie

University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

105

Pages:

1
Author:

Alayna Ibarra

Workshop #27 1. Integrate. Z 2 2 x (a) + dx x 2 1 Z 2 2 π (b) − ex 2 x 1 Z 4 3x − 4 √ (c) dx x 1 2. Find dy dx at (1, 1) for the curve y x + exy = ey + x. 3. At what point on the graph of f (x) = 9 x + 6 ln x is the tangent line parallel to the line y = x − 5? 4. A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft. below the level of the pier and the cable is pulled in at the rate of 36 ft/min, how fast is the boat moving when it is 48 feet from the base of the pier? 5. Use the graph of f , shown below, to find the following. (a) lim f (x) x→∞ (b) lim f 0 (x) (c) (d) (e) (f) (g) x→∞ 0 f (1) Find a value of x for which f 0 (x) = 12 . For what approximate values of x is the graph of f concave downward? Find a value of x for which f 0 (x) < 0 and f 00 (x) > 0. Where are the inflection points on the graph?

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