5. Let f [0,2] R be defined by x, 0 < x < 1 f(x) = x+1 1≤x≤2 (a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to. (b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2]. (c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification. (d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.
5. Let f [0,2] R be defined by x, 0 < x < 1 f(x) = x+1 1≤x≤2 (a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to. (b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2]. (c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification. (d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Let f : [0, 2] → R be defined by
f (x) =
{
x, 0 ≤ x < 1
x + 1 1 ≤ x ≤ 2
(a) Explain why f ∈ R[0, 2] by identifying the class of functions f belongs to.
(b) Determine explicitly the function F (x) =
∫ x
0
f (t)dt for x ∈ [0, 2].
(c) Find the subset {x : F is continuous at x} ⊆ [0, 2] with your justification.
(d) Find the subset {x : F is
PROVE THE FOLLOWING IN THE PICTURE, WHILE ALSO EXPLAINING EACH STEP IN FULL DETAIL
![5. Let f [0,2] R be defined by
x,
0 < x < 1
f(x)
=
x+1
1≤x≤2
(a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to.
(b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2].
(c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification.
(d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643c9073-bfc9-41d3-b50c-3b14187fea75%2F27ca5aee-6b01-46c4-b8bf-dc837ec4fd19%2Fmo5vjgn_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let f [0,2] R be defined by
x,
0 < x < 1
f(x)
=
x+1
1≤x≤2
(a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to.
(b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2].
(c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification.
(d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.
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