Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Transcribed Image Text:Find and simplify the function values.
f(x, у) %3D 8х + у2
Exercise (a)
f(x + Дх, у) — f(x, у)
Ax
Step 1
First, to find f(x + Ax, y),substitutex + Ax for x in f(x, y) and simplify.
f(x + Ax, y)
8( x + Ax
+ y2
x + Ar
8x + y“ + Ax X
8x + 8Ar+ y?
Step 2
You have found f(x + Ax, y)
= 8x + 8Ax + y2. Simplify to find the function value.
22) - (sx + v²)
f(x + Дх, у) — f(x, y)
8х + 8Дх +
Ax
Ax
Ax
Ax
Ax # 0
II

Transcribed Image Text:Exercise (b)
f(x, y + Ay) – f(x, y)
Ду
Step 1
First, to find f(x, y + Ay), substitute y + Ay for y in f(x, y) and simplify.
2
f(x, у + Ду)
8х + ( Ду
y + Ay
8х +
,2
+ (Ay)2
y? + 2 · y · Ay
Step 2
You have found f(x, y + Ay) = 8x + y2 + 2yAy + (Ay)². Simplify to find the function value.
f(x, у + Ду) — f(x, у)
Ду
8x + y² + 2yAy + (Ay)?) – (8x
8х + y2
Ду
2
Ду +
Ду
, Ду # 0
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