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Let f be a real function continuous on its domain D = dom(f). Suppose that D contains a neighborhood of a E R. Which of the following is false ? AIM: To demonstrate understanding of the definition of continuous functions, as well as properties of operations on continuous functions The map g(x) a. is continuous on D 6+5 b. The function h(x) cos[f(æ)] is (f(x))* +3 continuous on the whole of D. c. If (æn) is a sequence in D converging to a and h(x) = e" f(x), then lim, 00 h(æn) = e“ f(a). d. The map D → R: x → f(x) is er continuous on D e. Vz e D, lim, 2 f(x) = f(z). f. The function R(x) = f(x)/x may not be continuous on the whole of D.

Let f be a real function continuous on its domain D = dom(f). Suppose that D contains a neighborhood of a E R. Which of the following is false ? AIM: To demonstrate understanding of the definition of continuous functions, as well as properties of operations on continuous functions The map g(x) a. is continuous on D 6+5 b. The function h(x) cos[f(æ)] is (f(x))* +3 continuous on the whole of D. c. If (æn) is a sequence in D converging to a and h(x) = e" f(x), then lim, 00 h(æn) = e“ f(a). d. The map D → R: x → f(x) is er continuous on D e. Vz e D, lim, 2 f(x) = f(z). f. The function R(x) = f(x)/x may not be continuous on the whole of D.

Advanced Engineering Mathematics
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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Let f be a real function continuous on its domain D = dom(f). Suppose that D contains a neighborhood of a E R. Which of the following is false ? AIM: To demonstrate understanding of the definition of continuous functions, as well as properties of operations on continuous functions a. The map g(x) is continuous on D cos[f(x)] is (f(x))* +3 b. The function h(x) continuous on the whole of D. c. If (xn) is a sequence in D converging to a and h(x) = e" f(x), then lim, -00 h(xn) = e“ f(a). d. The map D → R: x → f(x) is continuous on D e. Vz E D, lim,→z f(x) = f(z). %3D O f. The function R(x) = f(x)/x may not be continuous on the whole of D.
Transcribed Image Text:Let f be a real function continuous on its domain D = dom(f). Suppose that D contains a neighborhood of a E R. Which of the following is false ? AIM: To demonstrate understanding of the definition of continuous functions, as well as properties of operations on continuous functions a. The map g(x) is continuous on D cos[f(x)] is (f(x))* +3 b. The function h(x) continuous on the whole of D. c. If (xn) is a sequence in D converging to a and h(x) = e" f(x), then lim, -00 h(xn) = e“ f(a). d. The map D → R: x → f(x) is continuous on D e. Vz E D, lim,→z f(x) = f(z). %3D O f. The function R(x) = f(x)/x may not be continuous on the whole of D.
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