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

Sagot :

Space

Answer:

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]

General Formulas and Concepts:

Algebra I

Terms/Coefficients

  • Factoring

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5}[/tex]

Step 2: Evaluate

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

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

Unit: Limits

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