Find lim_(x rarr oo)(x^(2)-4)/(x+4). Choose 1 answer: (A) 1 (B) -1 (C) 0 (D) The limit is unbounded

Analyze degrees of polynomials: To find the limit of the given function as x approaches infinity, we can analyze the degrees of the polynomials in the numerator and the denominator. The degree of the polynomial in the numerator (x^2 - 4) is 2. The degree of the polynomial in the denominator (x + 4) is 1. Since the degree of the numerator is higher than the degree of the denominator, we can expect the limit to be unbounded.Divide terms to simplify expression: To confirm our expectation, we can divide each term in the numerator by x, the highest power of x in the denominator, to simplify the expression. This gives us (x^2/x - 4/x) / (x/x + 4/x). Simplifying this, we get (x - 4/x) / (1 + 4/x).Simplify expression: As x approaches infinity, the terms 4/x in the numerator and 4/x in the denominator approach 0. So the expression simplifies to x / 1, which is just x.Approach of terms as x approaches infinity: Since x approaches infinity, the limit of the function as x approaches infinity is also infinity. Therefore, the limit is unbounded.

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Find
lim_(x rarr oo)(x^(2)-4)/(x+4).
Choose 1 answer:
(A) 1
(B) -1
(C) 0
(D) The limit is unbounded

Find $\lim _{x \rightarrow \infty} \frac{x^{2}-4}{x+4}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $-1$ $\newline$ (C) $0$ $\newline$ (D) The limit is unbounded

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Precalculus

Find limits of polynomials and rational functions

Full solution

Q. Find

\lim _{x \rightarrow \infty} \frac{x^{2}-4}{x+4}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

-1

\newline

(C)

0

\newline

(D) The limit is unbounded

Analyze degrees of polynomials: To find the limit of the given function as $x$ approaches infinity, we can analyze the degrees of the polynomials in the numerator and the denominator. $\newline$ The degree of the polynomial in the numerator ( $x^2 - 4$ ) is $2$ . $\newline$ The degree of the polynomial in the denominator ( $x + 4$ ) is $1$ . $\newline$ Since the degree of the numerator is higher than the degree of the denominator, we can expect the limit to be unbounded.
Divide terms to simplify expression: To confirm our expectation, we can divide each term in the numerator by $x$ , the highest power of $x$ in the denominator, to simplify the expression. $\newline$ This gives us $(\frac{x^2}{x} - \frac{4}{x}) / (\frac{x}{x} + \frac{4}{x})$ . $\newline$ Simplifying this, we get $(x - \frac{4}{x}) / (1 + \frac{4}{x})$ .
Simplify expression: As $x$ approaches infinity, the terms $\frac{4}{x}$ in the numerator and $\frac{4}{x}$ in the denominator approach $0$ . So the expression simplifies to $\frac{x}{1}$ , which is just $x$ .
Approach of terms as $x$ approaches infinity: Since $x$ approaches infinity, the limit of the function as $x$ approaches infinity is also infinity. $\newline$ Therefore, the limit is unbounded.