Consider the following functions. G(x)=x²; f(x) = 4x² (a) Verify that G is an antiderivative of f. O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x OG(x) is an antiderivative of f(x) because f(x)=G(x) + C for all x OG(x) is an antiderivative of f(x) because f(x)=G(x) for all x. OG(x) is an antiderivative of f(x) because G(x) = f(x) for all x. (b) Find all antiderivatives of f. (Use C for the constant of integration.) (c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). 10 -10 10 st -10
Consider the following functions. G(x)=x²; f(x) = 4x² (a) Verify that G is an antiderivative of f. O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x OG(x) is an antiderivative of f(x) because f(x)=G(x) + C for all x OG(x) is an antiderivative of f(x) because f(x)=G(x) for all x. OG(x) is an antiderivative of f(x) because G(x) = f(x) for all x. (b) Find all antiderivatives of f. (Use C for the constant of integration.) (c) Sketch the graphs of a few members of the family of antiderivatives found in part (b). 10 -10 10 st -10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6.1 Q3
Transcribed Image Text:Consider the following functions.
G(x)=x²; f(x) = 4x²
(a) Verify that G is an antiderivative of f.
O G(x) is an antiderivative of f(x) because G(x) = f(x) for all x
OG(x) is an antiderivative of f(x) because f(x)=G(x) + C for all x
OG(x) is an antiderivative of f(x) because f(x)=G(x) for all x.
OG(x) is an antiderivative of f(x) because G(x) = f(x) for all x.
(b) Find all antiderivatives of f. (Use C for the constant of integration.)
(c) Sketch the graphs of a few members of the family of antiderivatives found in part (b).
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10
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