Question

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

Answer 1

`\displaystyle \lim_(x \to 3^+) f(x) = 2`

General Formulas and Concepts:

Calculus

Limits

• Right-Side Limit:
  `\displaystyle \lim_(x \to c^+) f(x)`
• Left-Side Limit:
  `\displaystyle \lim_(x \to c^-) f(x)`

Graphical Limits

Explanation:

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

`\displaystyle \lim_(x \to 3^+) f(x)`

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
`\displaystyle \text{f(x)}` approaches x= 3, we have f(x) approaching 2.

∴
`\displaystyle \lim_(x \to 3^+) f(x) = 2`

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

Unit: Limits