Investigating A Limit Via Graph

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Homework Statement
Graphs and Limits
Relevant Equations
Quadratic and Piecewise Function
Use the graph to investigate

(a) lim of f(x) as x→2 from the left side.

(b) lim of f(x) as x→2 from the right side.

(c) lim of f(x) as x→2.

Question 18

For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

For part (b), as I travel along on the x-axis coming from the right, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

For part (c), as I travel along on the x-axis coming from the left and right simultaneously, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

I conclude that the limit is 4.

You say?

I will answer 20 on a separate thread.
 

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nycmathguy said:
Question 18

For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?
Correct. The left-side limit if 4, and the presence of a hole doesn't matter.
nycmathguy said:
For part (b), as I travel along on the x-axis coming from the right, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?
Correct. The right-side limit if 4, and the presence of a hole doesn't matter.
nycmathguy said:
For part (c), as I travel along on the x-axis coming from the left and right simultaneously, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

I conclude that the limit is 4.
Yes, correct.
 
Mark44 said:
Correct. The left-side limit if 4, and the presence of a hole doesn't matter.
Correct. The right-side limit if 4, and the presence of a hole doesn't matter.
Yes, correct.

I finally get one right on my own.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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