3. For each statement, determine whether it is TRUE or FALSE. (Enter T or F in the middle of the box) (a) Let f be a function defined on R. If f2 is continuous at a, then f is continuous at a. (b) Let f, g, and h be functions defined on R and let a Є R. If VxR, f(x)g(x) ≤ h(x), ⚫lima f(x) exists and lima h(x) = ∞, then lima 9(x) exists or is oo. Let f and g be functions defined on R and let a € R. If lima f(x)g(x) = 0, then lima f(x) = 0 and lim→a 9(x) = 0.
3. For each statement, determine whether it is TRUE or FALSE. (Enter T or F in the middle of the box) (a) Let f be a function defined on R. If f2 is continuous at a, then f is continuous at a. (b) Let f, g, and h be functions defined on R and let a Є R. If VxR, f(x)g(x) ≤ h(x), ⚫lima f(x) exists and lima h(x) = ∞, then lima 9(x) exists or is oo. Let f and g be functions defined on R and let a € R. If lima f(x)g(x) = 0, then lima f(x) = 0 and lim→a 9(x) = 0.
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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Transcribed Image Text:3. For each statement, determine whether it is TRUE or FALSE. (Enter T or F in the middle of the box)
(a)
Let f be a function defined on R. If f2 is continuous at a, then f is continuous at a.
(b)
Let f, g, and h be functions defined on R and let a Є R. If
VxR, f(x)g(x) ≤ h(x),
⚫lima f(x) exists and lima h(x) = ∞,
then lima 9(x) exists or is oo.
Let f and g be functions defined on R and let a € R.
If lima f(x)g(x) = 0, then lima f(x) = 0 and lim→a 9(x) = 0.
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