(a) Let f: [0, ∞) → R be defined by f(x) = √x. Show that lim f(x) ce [0, ∞). Is f a continuous function? 24x = √e for all (Remark: You may use the fact that 0 ≤ a < b if and only if √a < √b. As a hint on how to play the & games, look at the proof of Proposition 2.2.6 in the textbook.) (b) Let f: R → R be defined by f(x) := cos(x). Show that lim f(x) = cos(c) for all c € R. Is f a continuous function? X-C (Remark: You may use trigonometric identities here, and the fact that |sin(x)| ≤ |x|, and |sin(x)| ≤ 1 for all x € R. See Example 3.2.6 in the textbook for the necessary algebra; however, you will need explain all of the steps of the proof to receive credit.)
(a) Let f: [0, ∞) → R be defined by f(x) = √x. Show that lim f(x) ce [0, ∞). Is f a continuous function? 24x = √e for all (Remark: You may use the fact that 0 ≤ a < b if and only if √a < √b. As a hint on how to play the & games, look at the proof of Proposition 2.2.6 in the textbook.) (b) Let f: R → R be defined by f(x) := cos(x). Show that lim f(x) = cos(c) for all c € R. Is f a continuous function? X-C (Remark: You may use trigonometric identities here, and the fact that |sin(x)| ≤ |x|, and |sin(x)| ≤ 1 for all x € R. See Example 3.2.6 in the textbook for the necessary algebra; however, you will need explain all of the steps of the proof to receive credit.)
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 2CR
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