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Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x+√√√x-9, For a 9, we have lim f(x) lim (x+√√x-9) x-a x-a = lim (x) + lim = x-a x-a lim (x) + V x-a = lim (x) + x-a lim x-a lim x-a [9,00) by the sum law by the root law lim (9) by the difference law x-a = = - 9 by the direct substitution property Therefore, f is continuous at x = a for every a in (9, 0). Also, lim¸ f(x) = x-9- = f(9), so f is continuous from the right at 9. Thus, f is continuous on [9,∞).

Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x+√√√x-9, For a 9, we have lim f(x) lim (x+√√x-9) x-a x-a = lim (x) + lim = x-a x-a lim (x) + V x-a = lim (x) + x-a lim x-a lim x-a [9,00) by the sum law by the root law lim (9) by the difference law x-a = = - 9 by the direct substitution property Therefore, f is continuous at x = a for every a in (9, 0). Also, lim¸ f(x) = x-9- = f(9), so f is continuous from the right at 9. Thus, f is continuous on [9,∞).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 6CR
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Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x+√√√x-9, For a 9, we have lim f(x) lim (x+√√x-9) x-a x-a = lim (x) + lim = x-a x-a lim (x) + V x-a = lim (x) + x-a lim x-a lim x-a [9,00) by the sum law by the root law lim (9) by the difference law x-a = = - 9 by the direct substitution property Therefore, f is continuous at x = a for every a in (9, 0). Also, lim¸ f(x) = x-9- = f(9), so f is continuous from the right at 9. Thus, f is continuous on [9,∞).
Transcribed Image Text:Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x+√√√x-9, For a 9, we have lim f(x) lim (x+√√x-9) x-a x-a = lim (x) + lim = x-a x-a lim (x) + V x-a = lim (x) + x-a lim x-a lim x-a [9,00) by the sum law by the root law lim (9) by the difference law x-a = = - 9 by the direct substitution property Therefore, f is continuous at x = a for every a in (9, 0). Also, lim¸ f(x) = x-9- = f(9), so f is continuous from the right at 9. Thus, f is continuous on [9,∞).
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