ƒ'(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 X Match each of the following mathematical expressions with the correct description. Each description should be used once.
ƒ'(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 X Match each of the following mathematical expressions with the correct description. Each description should be used once.
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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having trouble with question 1,2,4
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.
![1. f(x+h) − f(x) represents
[Select]
2. h represents [Select]
f(x + h) - f(x)
h
3.
B
4. lim
h→0
represents
f(x+h)-f(x)
h
[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)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67fbd5d8-0948-4b18-8071-fc784645c75f%2Fbb3a3711-3ccb-49af-baeb-96fc3c9f6b82%2Fri588c1_processed.png&w=3840&q=75)
Transcribed Image Text:1. f(x+h) − f(x) represents
[Select]
2. h represents [Select]
f(x + h) - f(x)
h
3.
B
4. lim
h→0
represents
f(x+h)-f(x)
h
[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)).
Expert Solution
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