Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.1 Exercises - Page 876: 9

Answer

The solutions are a) $f(5,0) = 5.$ b) $f(3,2) = 3e^2.$ c) $f(2,-1) = \frac{2}{e}.$ d) $f(5,y) = 5e^y.$ e) $f(x,2) = xe^2.$ f) $f(t,t) = te^t.$

Work Step by Step

We will simply substitute $x$ from the first coordinate of a given point and $y$ from the second coordinate from the given point into the $f(x,y)=xe^y$. a) $f(5,0) = 5\times e^0 = 5.$ b) $f(3,2) = 3\times e^2 = 3e^2.$ c) $f(2,-1) = 2\times e^{-1} = \frac{2}{e}.$ d) $f(5,y) = 5\times e^y = 5e^y.$ e) $f(x,2) = x\times e^2 = xe^2.$ f) $f(t,t) = te^t.$
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