Consider the function f (x) given by f(x) = {kx, if x < 1; 0 if x = 1; 2k-kx if x > 1}, where k > 0 is a constant. a) For each of the three conditions for continuity, determine whether it is satisfied at point x = 1. b) Based on a), is f(x) continuous at x = 1? Does limx->1f(x) exsist? Is limitx->1f(x)=f(1)?
Consider the function f (x) given by f(x) = {kx, if x < 1; 0 if x = 1; 2k-kx if x > 1}, where k > 0 is a constant. a) For each of the three conditions for continuity, determine whether it is satisfied at point x = 1. b) Based on a), is f(x) continuous at x = 1? Does limx->1f(x) exsist? Is limitx->1f(x)=f(1)?
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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Consider the function f (x) given by f(x) = {kx, if x < 1; 0 if x = 1; 2k-kx if x > 1}, where k > 0 is a constant.
a) For each of the three conditions for continuity, determine whether it is satisfied at point x = 1.
b) Based on a), is f(x) continuous at x = 1? Does limx->1f(x) exsist? Is limitx->1f(x)=f(1)?
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