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9. Let f(x) = x². Compute a value & such that if |x-1|

9. Let f(x) = x². Compute a value & such that if |x-1|

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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Question 9.

8. For a real number c, let f(x) (b) Calculate lim f(x). +4←x (a) Calculate lim f(x) as an expression in the parameter c. X-T YA (c) For which value(s) of c does lim f(x) exist? X→π 1.5 = 9. Let f(x) = x². Compute a value d such that if |x − 1| < 8 then |x² − 1| < . The question is illustrated below. 1 √x² + c 2 sin (2) 0.5 0 if 0 < x < T if x ≥ π ? 3 1 ? 10. Using the precise definition of a limit, with & and d, prove lim 2x² - 4x + 1 = −1. x→1 y=x²
Transcribed Image Text:8. For a real number c, let f(x) (b) Calculate lim f(x). +4←x (a) Calculate lim f(x) as an expression in the parameter c. X-T YA (c) For which value(s) of c does lim f(x) exist? X→π 1.5 = 9. Let f(x) = x². Compute a value d such that if |x − 1| < 8 then |x² − 1| < . The question is illustrated below. 1 √x² + c 2 sin (2) 0.5 0 if 0 < x < T if x ≥ π ? 3 1 ? 10. Using the precise definition of a limit, with & and d, prove lim 2x² - 4x + 1 = −1. x→1 y=x²
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