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Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the right of f of x. .

Sagot :

Answer:  3

Explanation:

Refer to the graph below. It should be similar to what your teacher gave you, based off the description.

Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.

As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.

In terms of notation, we can write [tex]\displaystyle \lim_{x\to3^{+}}f(x) = 3[/tex]

The portion [tex]x \to 3^{+}[/tex] means we're approaching 3 from the positive side, aka the right hand side on the number line.

View image jimthompson5910
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