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3. f(x + h) - f(x) h [Select] represents

3. f(x + h) - f(x) h [Select] represents

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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1. f(x+h) − f(x) represents [Select] 2. h represents [Select] 3. f(x+h)-f(x) h [Select] represents f(x+h)-f(x) h 4. lim h→0 [Select] represents Possible descriptions: A. the slope of the tangent line at the point (x, f(x)). B. the slope of the secant line joining the points (x, f(x)) and (x+h, f(x + h)). C. the vertical distance (the "rise") between the points (x, f(x)) and (x + h, f(x + h)). D. the horizontal distance (the "run") between the points (x, f(x)) and (x + h, f(x + h)).
Transcribed Image Text:1. f(x+h) − f(x) represents [Select] 2. h represents [Select] 3. f(x+h)-f(x) h [Select] represents f(x+h)-f(x) h 4. lim h→0 [Select] represents Possible descriptions: A. the slope of the tangent line at the point (x, f(x)). B. the slope of the secant line joining the points (x, f(x)) and (x+h, f(x + h)). C. the vertical distance (the "rise") between the points (x, f(x)) and (x + h, f(x + h)). D. the horizontal distance (the "run") between the points (x, f(x)) and (x + h, f(x + h)).
f'(x) = lim h→0 f(x+h)-f(x) h The goal of this problem is to break down this definition into pieces and understand their geometric meaning. Consider the diagram below (similar to the first diagram on page 1 of the notes): P(x, f(x)) X y = f(x) Q(x+ h, f(x + h)) Horizontal distance (run) Vertical distance (rise) x + h Match each of the following mathematical expressions with the correct description. Each description should be used once.
Transcribed Image Text:f'(x) = lim h→0 f(x+h)-f(x) h The goal of this problem is to break down this definition into pieces and understand their geometric meaning. Consider the diagram below (similar to the first diagram on page 1 of the notes): P(x, f(x)) X y = f(x) Q(x+ h, f(x + h)) Horizontal distance (run) Vertical distance (rise) x + h Match each of the following mathematical expressions with the correct description. Each description should be used once.
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