28) To evaluate S dt we could use the substitution a) t = sin(u) b) t = tan(u) c) t = sec(u) d) t = sec(u) tan(u)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve both 28 and 29 please

28) To evaluate f dt we could use the substitution
a) t = sin(u)
b) t = tan(u)
c) t = sec(u)
d) t = sec(u) tan(u)
29) Consider the function
2 if x =
1
f(x)
= {
1 if x E [0, 1] and x +
Which of the following statements are true?
a) f is integrable on [0, 1] and f(t)dt = 1.
b) If H(x) = S f(t)dt, then H is discontinuous at x = } because f is not continuous
at x =
2.
c) If H(x) = K f(t)dt, then H is continuous on [0,1] but is not differentiable at
- because f is not continuous at x =
1
21
d) If H(x) = S f(t)dt, then H is differentiable at x =} with H'(G) = 2.
e) If H(x) = S“ f(t)dt, then H is differentiable at x =
2
글 with H'()) = 1.
Transcribed Image Text:28) To evaluate f dt we could use the substitution a) t = sin(u) b) t = tan(u) c) t = sec(u) d) t = sec(u) tan(u) 29) Consider the function 2 if x = 1 f(x) = { 1 if x E [0, 1] and x + Which of the following statements are true? a) f is integrable on [0, 1] and f(t)dt = 1. b) If H(x) = S f(t)dt, then H is discontinuous at x = } because f is not continuous at x = 2. c) If H(x) = K f(t)dt, then H is continuous on [0,1] but is not differentiable at - because f is not continuous at x = 1 21 d) If H(x) = S f(t)dt, then H is differentiable at x =} with H'(G) = 2. e) If H(x) = S“ f(t)dt, then H is differentiable at x = 2 글 with H'()) = 1.
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