Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 13 - Partial Derivatives - 13.1 Functions Of Two Or More Variables - Exercises Set 13.1: 1

Answer

(a) $f(2,1)=5$, (b) $f(1,2)=3$, (c) $f(0,0)=1$, (d) $f(1,-3)=-2$, (e) $f(3a,a)=9a^3+1$, (f) $f(ab,a-b)=(ab)^2(a-b)+1$

Work Step by Step

(a) Substitute $x=2$ and $y=1:$ $$f(2,1)=2^2\cdot1+1=4+1=5$$ (b)Substitute $x=1$ and $y=2:$ $$f(1,2)=1^2\cdot2+1=2+1=3$$ (c)Substitute $x=0$ and $y=0:$ $$f(0,0)=0^2\cdot0+1=0+1=1$$ (d) Substitute $x=1$ and $y=-3:$ $$f(1,-3)=1^2\cdot(-3)+1=-3+1=-2$$ (e) Substitute $x=3a$ and $y=a:$ $$f(3a,a)=(3a)^2\cdot a+1=9a^3+1$$ (f) Substitute $x=ab$ and $y=a-b:$ $$f(ab,a-b)=(ab)^2\cdot(a-b)+1$$
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