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)?
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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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