Write a chain rule formula for the following derivative.
for u = f(r, s, t); r = g(y), s = h(z), t = k(x, z)
A. =
B. =
C. = 0
D. =
Answer: D
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Use the Concavity Theorem to determine where the given function is concave up and where it is concave down. Also find all inflection points.f(x) = x2 - 16x + 69
A. Concave up on (8, ?), concave down on (-?, 8); inflection point (8, 5) B. Concave up on (-?, 8), concave down on (8, ?); inflection point (8, 5) C. Concave down for all x; no inflection points D. Concave up for all x; no inflection points
Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0).f(x, y) =
A. 2 B. 0 C. 1 D. No limit
Simplify the polynomial by adding or subtracting, as indicated. Express your answer as a single polynomial in standard form.(7x5 + 8x2) + (6x5 - 4x2)
A. 17x14 B. 17x7 C. 13x5 + 4x2 D. 13x10 + 4x4
What area will Sam need to cover with black paint on his dartboard? Give the exact answer.
Sam is sketching a template on graph paper to use as a guide for his painted cork dart board. The diameter of Circle 1 is 2 feet and the distance between the edges of each of the next three pairs of circles is 1 foot.The distance between Circle 4 and Circle 5 is foot. Sam does not want axes through or touching his template and therefore wishes to sketch the dart board only in Quadrant I.At the closest points, he wants Circle 5 to be 1 unit from the y-axis and 1-unit from the x-axis. In this case: