Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Let g(x)=(2)/(x+3). Select the correct description of the one-sided limits of g at x=-3. Choose 1 answer: (A) {:[lim_(x rarr-3^(+))g(x)=+oo" and "],[lim_(x rarr-3^(-))g(x)=+oo]:} (B) {:[lim_(x rarr-3^(+))g(x)=+oo" and "],[lim_(x rarr-3^(-))g(x)=-oo]:} (C) {:[lim_(x rarr-3^(+))g(x)=-oo" and "],[lim_(x rarr-3^(-))g(x)=+oo]:} (D {:[lim_(x rarr-3^(+))g(x)=-oo" and "],[lim_(x rarr-3^(-))g(x)=-oo]:}$

Let $g(x)=\frac{2}{x+3}$ . $\newline$ Select the correct description of the one-sided limits of $g$ at $x=-3$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=+\infty \end{array}$ $\newline$ (B) $\newline$ $\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=-\infty \end{array}$ $\newline$ (C) $\newline$ $\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=+\infty \end{array}$ $\newline$ (D $\newline$ $\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=-\infty \end{array}$

View step-by-step help

Home

Math Problems

Algebra 2

Transformations of quadratic functions

Full solution

Q. Let

g(x)=\frac{2}{x+3}

\newline

Select the correct description of the one-sided limits of

g

x=-3

\newline

Choose

1

answer:

\newline

(A)

\newline

\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=+\infty \end{array}

\newline

(B)

\newline

\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=-\infty \end{array}

\newline

(C)

\newline

\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=+\infty \end{array}

\newline

\newline

\begin{array}{l} \lim _{x \rightarrow-3^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow-3^{-}} g(x)=-\infty \end{array}

Approach Analysis: To find the one-sided limits of $g(x)$ as $x$ approaches $-3$ , we need to consider the behavior of the function as $x$ gets very close to $-3$ from both the left ( $x \to -3^-$ ) and the right ( $x \to -3^+$ ).
Right Limit Calculation: First, let's consider the limit as $x$ approaches $-3$ from the right ( $x \to -3^+$ ). As $x$ gets closer to $-3$ from the right, the denominator ( $x+3$ ) gets closer to $0$ and the value of $g(x)$ increases without bound. Since the numerator is positive ( $2$ ), the function approaches positive infinity.
Left Limit Calculation: Now, let's calculate the limit as $x$ approaches $-3$ from the left ( $x \to -3^-$ ). As $x$ gets closer to $-3$ from the left, the denominator ( $x+3$ ) again gets closer to $0$ , but now from the negative side. This means that the value of $g(x)$ decreases without bound. Since the numerator is positive ( $2$ ), the function approaches negative infinity.
Final Results: Based on the calculations, the one-sided limits of $g(x)$ as $x$ approaches $-3$ are as follows: $\newline$ $\lim_{x \to -3^+} g(x) = +\infty$ $\newline$ $\lim_{x \to -3^-} g(x) = -\infty$