Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Textbook Question
Chapter 14.4, Problem 14E
In Exercises 1–14, find the gradient of the function. Assume the variables are restricted to a domain on which the function is defined.
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Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Chapter 14 Solutions
Calculus: Single And Multivariable
Ch. 14.1 - Using dierence quotients, estimate fx(3, 2) fy(3,...Ch. 14.1 - Prob. 3ECh. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - Approximate fx (3, 5) using the contour diagram of...Ch. 14.1 - Figure 14.11 shows the contour diagram of g(x, y)...Ch. 14.1 - Figure 14.13 shows the saddle-shaped surface z =...Ch. 14.2 - Prob. 2ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 8E
Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 65ECh. 14.2 - Which of the following functions satisfy the...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - Prob. 23ECh. 14.3 - In Exercises 2124, assume points P and Q are...Ch. 14.3 - The tangent plane to z = f(x, y) at the point (1,...Ch. 14.3 - Find an equation for the tangent plane to z = f(x,...Ch. 14.3 - (a). Find the equation of the plane tangent to the...Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - Prob. 45ECh. 14.4 - Prob. 48ECh. 14.4 - In Exercises 5051, nd the dierential df from the...Ch. 14.4 - In Exercises 5253, nd grad f from the dierential....Ch. 14.4 - In Problems 5864, nd the quantity. Assume that g...Ch. 14.4 - For f(x,y)=(x+y)/(1+x2) nd the directional...Ch. 14.4 - Let f(x, y) = x2y3. At the point (1, 2), nd a...
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