If is defined on [a, co) and integrable on [a,c] for c>a and lim c-8a True O False f(1) dr = ∞o, then f is improperly integrable on [a, ∞o).
If is defined on [a, co) and integrable on [a,c] for c>a and lim c-8a True O False f(1) dr = ∞o, then f is improperly integrable on [a, ∞o).
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
![Iff is defined on [a, co ) and integrable on [a,c] for c> a and lim
c-8a
True
O False
If f is integrable on [a,b], then F(x) =
O True
False
True
O False
=[^ƒ«
a
Let / be a function bounded on [a,b] and let P= {xx,...} be a partition of [a, b]. The lower sum off with respect to P is L(S.P) = Em Ax.
Ax=₁-1-1
O True
O False
f(1) dr= ∞o, then f is improperly integrable on [a, co ).
f(t) dt for x = [a, b] is uniformly continuous on [a,b].
Let DC R. A function f:D-R is continuous at c E D iff for any sequence
The lower integral of a function f bounded on [a, b] is L(f) = inf{L(f,P): P is a partition of [a,b]), where L(f,P) is the lower sum off with respect to P.
O True
False
O True
ⒸFalse
where m = inf(f(x) : x (x,-₁,1} and
(x₁) in D that converges to c, the sequence
e (f(x)) c
converges to f(c).
Let f:D-R, where DCR, and let c ED'. Then limf(x)=LER iff there exists a sequence (x) in D that converges to c with x #c for all n EN such that the sequence
(()) converges to L.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2Ffd9127e9-47c4-4859-906d-037342b33738%2Fokidv1a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Iff is defined on [a, co ) and integrable on [a,c] for c> a and lim
c-8a
True
O False
If f is integrable on [a,b], then F(x) =
O True
False
True
O False
=[^ƒ«
a
Let / be a function bounded on [a,b] and let P= {xx,...} be a partition of [a, b]. The lower sum off with respect to P is L(S.P) = Em Ax.
Ax=₁-1-1
O True
O False
f(1) dr= ∞o, then f is improperly integrable on [a, co ).
f(t) dt for x = [a, b] is uniformly continuous on [a,b].
Let DC R. A function f:D-R is continuous at c E D iff for any sequence
The lower integral of a function f bounded on [a, b] is L(f) = inf{L(f,P): P is a partition of [a,b]), where L(f,P) is the lower sum off with respect to P.
O True
False
O True
ⒸFalse
where m = inf(f(x) : x (x,-₁,1} and
(x₁) in D that converges to c, the sequence
e (f(x)) c
converges to f(c).
Let f:D-R, where DCR, and let c ED'. Then limf(x)=LER iff there exists a sequence (x) in D that converges to c with x #c for all n EN such that the sequence
(()) converges to L.
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