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Limits and Continuity Questions

Please help with the following problem. Provide step by step calculations.

True or false:

a)lim x--->2- f(x) = 3
b)limx--->2+ f(x) =0
c)lim x--->2- f(x) = lim x--->2+ f(x)
d) lim x--->2 f(x) exists
e) lim x--->4 f(x) exists
f) lim x--->4 f(x) = f(4)
g) f is continuous at x=4
h) f is continuous at x=0
i) lim x--->3 f(x) = lim x--->5 f(x)
j) f is continuous at x = 2

See attached file for diagram.

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Solution Preview

First, a definition...

A function f(x) is continuous at x = c if the following are true:

1) f(c) exists
2) the limit lim f(x) exists (it is the same from the left and the right)
x  c
3) the limit is equal to the value of f(c)

True or false:

a)lim x--->2- f(x) = 3

FALSE. The limit of f(x) as x approaches 2 from the left is equal to 0.

b)limx--->2+ f(x) =0 ...

Solution Summary

The following posting helps with problems involving limits. The solution consists of the definition of continuity of a function and answers to each part of the question. Step by step calculations are given for each problem.