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Let c ER and lim f²(x) = L, where L Є R. х-с 1. Prove: if L = 0, then lim f(x) = 0. x c 2. Prove: if L 0, then lim f(x) may not exist in R.

Let c ER and lim f²(x) = L, where L Є R. х-с 1. Prove: if L = 0, then lim f(x) = 0. x c 2. Prove: if L 0, then lim f(x) may not exist in R.

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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Let c ER and lim f²(x) = L, where L Є R. х-с 1. Prove: if L = 0, then lim f(x) = 0. x c 2. Prove: if L 0, then lim f(x) may not exist in R.
Transcribed Image Text:Let c ER and lim f²(x) = L, where L Є R. х-с 1. Prove: if L = 0, then lim f(x) = 0. x c 2. Prove: if L 0, then lim f(x) may not exist in R.
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