Let N(z) and D(T) be polynomial functions. Let Q(z) = N(z) and R(x) = D(z) N(z) 2+1 %3D Suppose that f(x) is a real-valued function defined in a deleted neighborhood of a E R and lim, ya f(x)= L eR. Which of the following is false?
Let N(z) and D(T) be polynomial functions. Let Q(z) = N(z) and R(x) = D(z) N(z) 2+1 %3D Suppose that f(x) is a real-valued function defined in a deleted neighborhood of a E R and lim, ya f(x)= L eR. Which of the following is false?
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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Question
![Let N(z) and D(E) be polynomial functions.
Let Q(z) =
N(z)
and R(z) =
D(2)
N(z)
2+1"
Suppose that f() is a real-valued function defined in a
deleted neighborhood of a E R and lim, a f(x) = LE R.
Which of the following is false?
Note: This problem is more about an application of Corollary 4.5.
O A. lim,
QIf(= = Q(L)
O B. lim, sa NS(z)) – N(L)
O C. For all & > 0, there exists some o> 0 such that
(0< z - al < 8 → |N[f(x)] – N(L)| <e).
O D. limz a
N(L)
R[f(x)] =
L11
O E. For all e> 0, there exists some o> 0 such that if D(a)= (a-6, a + 8) \ {a}, then
N[f (D(a))| C B(N(L), =).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ab3a5b1-b090-483c-a078-42a6cefd7a06%2Fb5b5b46d-504e-4bdf-a4b6-442243b58594%2Fd0if9il_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let N(z) and D(E) be polynomial functions.
Let Q(z) =
N(z)
and R(z) =
D(2)
N(z)
2+1"
Suppose that f() is a real-valued function defined in a
deleted neighborhood of a E R and lim, a f(x) = LE R.
Which of the following is false?
Note: This problem is more about an application of Corollary 4.5.
O A. lim,
QIf(= = Q(L)
O B. lim, sa NS(z)) – N(L)
O C. For all & > 0, there exists some o> 0 such that
(0< z - al < 8 → |N[f(x)] – N(L)| <e).
O D. limz a
N(L)
R[f(x)] =
L11
O E. For all e> 0, there exists some o> 0 such that if D(a)= (a-6, a + 8) \ {a}, then
N[f (D(a))| C B(N(L), =).
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