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2.29 a. Suppose f is continuous at p and f(p) > c. Prove: There exists & > 0 such that x E D; n (p – 8, p+ 8) implies f(x) > c. (Hint: Consider g(x) = f(x) – c.) b. Suppose f is continuous at p and f(p) < c. Prove: There exists d > 0 such that x E D; n (p – 6, p+ 8) implies f(x) < c. (Hint: Consider g(x) = -f(x).) I underlined the difference between each part

2.29 a. Suppose f is continuous at p and f(p) > c. Prove: There exists & > 0 such that x E D; n (p – 8, p+ 8) implies f(x) > c. (Hint: Consider g(x) = f(x) – c.) b. Suppose f is continuous at p and f(p) < c. Prove: There exists d > 0 such that x E D; n (p – 6, p+ 8) implies f(x) < c. (Hint: Consider g(x) = -f(x).) I underlined the difference between each part

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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2.29 a. Suppose f is continuous at p and f(p) > c. Prove: There exists & > 0 such that x E D; n (p – 8, p+ 8) implies f(x) > c. (Hint: Consider g(x) = f(x) – c.) b. Suppose f is continuous at p and f(p) < c. Prove: There exists d > 0 such that x E D; n (p – 6, p+ 8) implies f(x) < c. (Hint: Consider g(x) = -f(x).) I underlined the difference between each part
Transcribed Image Text:2.29 a. Suppose f is continuous at p and f(p) > c. Prove: There exists & > 0 such that x E D; n (p – 8, p+ 8) implies f(x) > c. (Hint: Consider g(x) = f(x) – c.) b. Suppose f is continuous at p and f(p) < c. Prove: There exists d > 0 such that x E D; n (p – 6, p+ 8) implies f(x) < c. (Hint: Consider g(x) = -f(x).) I underlined the difference between each part
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