(a) Let h: S→ R and c be a cluster point of S. Show that if lim h(x) = L = 0, then there exists some > 0 such that for all x € (S\ {c}) n (c-8, c+d), h(x) ‡ 0. 2-c (b) Let h: S→ R be continuous and c be a cluster point of S. Show that if h(c) # 0, then there exists some AC S such that c is a cluster point of A, h|₁ (x) ‡0 for all x ¤ A, and 1 lim (ALA(2)) - 1 lim (h(x)) h(c) I-C =
(a) Let h: S→ R and c be a cluster point of S. Show that if lim h(x) = L = 0, then there exists some > 0 such that for all x € (S\ {c}) n (c-8, c+d), h(x) ‡ 0. 2-c (b) Let h: S→ R be continuous and c be a cluster point of S. Show that if h(c) # 0, then there exists some AC S such that c is a cluster point of A, h|₁ (x) ‡0 for all x ¤ A, and 1 lim (ALA(2)) - 1 lim (h(x)) h(c) I-C =
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
Section3.1: Limits
Problem 66E
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