Let f:I-R, where I is an interval and z E I. Suppose lim [f(a+h)-f(x - h)] = 0. Does this mean f is continuous at r. Either prove or disprove by giving a counter example.
Let f:I-R, where I is an interval and z E I. Suppose lim [f(a+h)-f(x - h)] = 0. Does this mean f is continuous at r. Either prove or disprove by giving a counter example.
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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![Homework Set 4: Analysis
1. Let f:I-R, where I is an interval and IE I. Suppose
lim [f(a+h)-f(x-h)] = 0.
Does this mean f is continuous at r. Either prove or disprove by giving a counter example.
2. Let f:I-R, where I is an interval and r € I. Suppose
lim [f(r+h) + f(x-h)-2f(x)] = 0.
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Transcribed Image Text:Homework Set 4: Analysis
1. Let f:I-R, where I is an interval and IE I. Suppose
lim [f(a+h)-f(x-h)] = 0.
Does this mean f is continuous at r. Either prove or disprove by giving a counter example.
2. Let f:I-R, where I is an interval and r € I. Suppose
lim [f(r+h) + f(x-h)-2f(x)] = 0.
mole
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A function is continuos if Left limit = Right Limit = Function value at a point
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