Compute the following limit е (x,y) → (0,1) ex ज् :
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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![to the follow
Theorem 4 Properties of Continuous Functions Suppose that f: A C
R"→R", g: ACR"→ Rm, and let c be a real number.
(i) If f is continuous at xo, so is cf, where (cf)(x) = c[f(x)].
(ii) If f and g are continuous at xo, so is f + g, where the sum of f and g is
defined by (f+g)(x) = f(x) + g(x).
(iii) If f and g are continuous at xo and m =
defined by (fg)(x) = f(x)g(x) is continuous at Xo.
1, then the product function fg
(iv) If f: AC R" → R is continuous at xo and nowhere zero on A, then the
quotient 1/f is continuous at xo, where (1/f)(x) = 1/f(x).
(v) If f: ACR" → Rm and f(x) = (fi(x), ..., fm(x)), then f is continuous
at xo if and only if each of the real-valued functions fi, ..., fm is continuous
at Xo.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa03415f8-38f2-4478-b688-afaca619ca5c%2Ff5a22891-5ff3-4281-8e2d-9fd5676e1468%2Fossjh8q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:to the follow
Theorem 4 Properties of Continuous Functions Suppose that f: A C
R"→R", g: ACR"→ Rm, and let c be a real number.
(i) If f is continuous at xo, so is cf, where (cf)(x) = c[f(x)].
(ii) If f and g are continuous at xo, so is f + g, where the sum of f and g is
defined by (f+g)(x) = f(x) + g(x).
(iii) If f and g are continuous at xo and m =
defined by (fg)(x) = f(x)g(x) is continuous at Xo.
1, then the product function fg
(iv) If f: AC R" → R is continuous at xo and nowhere zero on A, then the
quotient 1/f is continuous at xo, where (1/f)(x) = 1/f(x).
(v) If f: ACR" → Rm and f(x) = (fi(x), ..., fm(x)), then f is continuous
at xo if and only if each of the real-valued functions fi, ..., fm is continuous
at Xo.
Transcribed Image Text:4.) Compute the following limits:
ety =
a.) limit
(x,y) → (0,1)
9
timil
(5,0) e (30)
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