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Find and simplify the function values. f(x, y) = 8x + y2 Exercise (a) f(x + Дх, у) — f(x, у) Дх

Find and simplify the function values. f(x, y) = 8x + y2 Exercise (a) f(x + Дх, у) — f(x, у) Дх

Calculus: Early Transcendentals
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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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: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
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
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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