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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![1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b).
2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a),
f(a+h, b), and f(a, b+ k) – f (a, b).
%3D
3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h,
and q = [f(x, y + k) – f(x, y)]/k.
%3D
SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES
411
4. Let f(x, y) = x² + 2xy + y².
(a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b).
(b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04536e59-763c-440c-af8f-4a3fc9711a35%2Fd3511c63-3f60-4b70-b0fe-c6b136f23094%2Flldydcb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b).
2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a),
f(a+h, b), and f(a, b+ k) – f (a, b).
%3D
3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h,
and q = [f(x, y + k) – f(x, y)]/k.
%3D
SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES
411
4. Let f(x, y) = x² + 2xy + y².
(a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b).
(b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.
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