Question

Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.

Answer 1

`\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty`

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:

If we graph the function, we can see that as we approach 3 from the left, we go towards negative infinity.

∴
`\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty`

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

Unit: Limits