Question

Find the limit of the function algebraically. Lim=-5 x^2-25/x+5

Answer 1

`\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5) = 0`

General Formulas and Concepts:

Algebra I

Terms/Coefficients

• Factoring

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
`\displaystyle \lim_(x \to c) x = c`

Explanation:

Step 1: Define

Identify

`\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5)`

Step 2: Evaluate

1. Factor:
   `\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5) = \lim_(x \to 5) ((x - 5)(x + 5))/(x + 5)`
2. Simplify:
   `\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5) = \lim_(x \to 5) x - 5`
3. Limit Rule [Variable Direct Substitution]:
   `\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5) = 5 - 5`
4. Simplify:
   `\displaystyle \lim_(x \to 5) (x^2 - 25)/(x + 5) = 0`

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

Unit: Limits