Question

now, evaluate the limit. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. (limlimits_{x \to 0} \frac{x^3 + 4x^2}{x^2} = ) (type an integer or a simplified fraction.)
b. the limit does not exist and is neither (infty) nor (-infty).

Explanation:

Step1: Simplify the expression

Factor out \(x^2\) from the numerator: \(\frac{x^3 + 4x^2}{x^2}=\frac{x^2(x + 4)}{x^2}\)
Cancel out \(x^2\) (for \(x
eq0\)): \(x + 4\)

Step2: Evaluate the limit as \(x\to0\)

Substitute \(x = 0\) into \(x + 4\): \(0 + 4 = 4\)

Answer:

\(4\)