University:
Whitman College
Course:
MATH-339 | Operations Research
Academic year:

2023
Views:

106

Pages:

2
Author:

Beeled9z

DGD3/MAT1339-S14 1. Differentiate with respect to t: (a) f (x) = 3 sin2 (2t − 4) − 2 cos2 (3t + 1). (b) g(x) = sin2 (cos(t)). (c) h(x) = 5t sin3 (2t − π). 2. Determine d2 y dx2 for y = x2 cos(x). 3. Determine the derivative of each function with respect to the variable indicated: (a) f (θ) = cos(sin(θ)) + sin(cos(θ)). (b) g(x) = cos2 (sin(x)). (c) h(θ) = cos(7θ) − cos2 (5θ). 1 4. A pond has a population of algae of 2000. After 15 min, the population is 4000. This population can be modelled by an equation of the form P = P0 at , where P is the population after t hours, and P0 is the initial population. (a) Determine the values of P0 and a. (b) Find the algae population after 10 min. (c) Find the rate of change of the algae population after one hour. 5. Differentiate with respect to x: (a) y = e2x − e−2x . (d) y = ecos x . (b) y = 4xex . (e) y = 2x2 ecos(2x) . (c) y = xe2x + 2e−3x . 6. Find the derivative of the following functions: (a) f (x) = 3x (cos(x) + x10 ) f 0 (x) = (b) g(x) = 5sin(2x)+cos(6x) . g 0 (x) = (c) h(x) = x3 − 2x esin(x) . h0 (x) = 2

DGD3-Math339-S14 - Study Guide

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