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Use the given graph to determine the limit, if it exists.
Find limit as x approaches three from the right of f of x.

7
1.5
Does not exist
2

Use The Given Graph To Determine The Limit If It Exists Find Limit As X Approaches Three From The Right Of F Of X 7 15 Does Not Exist 2 class=

Sagot :

Space

Answer:

[tex]\displaystyle \lim_{x \to 3^+} f(x) = 2[/tex]

General Formulas and Concepts:

Calculus

Limits

  • Right-Side Limit:                                                                                             [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]
  • Left-Side Limit:                                                                                               [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]

Graphical Limits

Step-by-step explanation:

We are given the limit and the graph of f(x):

[tex]\displaystyle \lim_{x \to 3^+} f(x)[/tex]

We are trying to find what the value of f(x) is when we approach x = 3 from the right. As we follow the piecewise function from the right, we see that as [tex]\displaystyle \text{f(x)}[/tex] approaches x= 3, we have f(x) approaching 2.

∴  [tex]\displaystyle \lim_{x \to 3^+} f(x) = 2[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

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