Answer:
c. 20
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
We are given the following limit:
[tex]\displaystyle \lim_{x \to 2} (3x^3 + x^2 - 8)[/tex]
Rewriting this limit using limit properties, we obtain:
[tex]\displaystyle \lim_{x \to 2} (3x^3 + x^2 - 8) = 3\lim_{x \to 2} x^3 + \lim_{x \to 2} x^2 - \lim_{x \to 2} 8[/tex]
Evaluate the limits using various limit rules:
[tex]\displaystyle \lim_{x \to 2} (3x^3 + x^2 - 8) = 3(2)^3 + (2)^2 - 8[/tex]
Simplify:
[tex]\displaystyle \lim_{x \to 2} (3x^3 + x^2 - 8) = 20[/tex]
And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
