21:I[49711,["/_next/static/chunks/0t1_7x_uuxe34.js","/_next/static/chunks/0~ta-e_o9dqvm.js","/_next/static/chunks/115lbazto1qq7.js","/_next/static/chunks/0vq81gpimz.3f.js","/_next/static/chunks/0jal2z51-yxb_.js"],"default"] 22:T4e0,A limit is the value that a function "approaches" as the input approaches some value. $\lim\limits_{x \to -8} g(x)$ is the limit of $g(x)$ as $x$ approaches $-8$. Let's look at the table and see if the $g(x)$-values seem to approach a distinct value as the $x$-values approach $-8$. [[table 1]] As the $x$-values *increase towards* $x=-8$ (i.e. approach it from the left), the $g(x)$-values seem to approach $0$. [[table 2]] As the x-values decrease towards $x = -8$ (i.e. approach it from the right), the $g(x)$-values seem to approach $0$. **A reasonable estimate for $\lim\limits_{x \to -8} g(x)$ is $0$.** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original exercise containing this question can be found here: Limits intro. Note: All Khan Academy content is available for free at www.khanacademy.org.23:T474,The expression $\lim\limits_{x \to 2^+} f(x) = 3$ states that the limit of $f$ as $x$ approaches $2$ from the right side is equal to $3$. **A** [[graph 1]] In graph A, $\lim\limits_{x \to 2^+} f(x)$ seems to equal to $1$. **B** [[graph 2]] In graph B, $\lim\limits_{x \to 2^+} f(x)$ seems to be equal to $3$. **C** [[graph 3]] In graph C, $\lim\limits_{x \to 2^+} f(x)$ seems to be equal to $3$ as well. **In conclusion, these graphs agree with $\lim\limits_{x \to 2^+} f(x) = 3$.** * **Graph B** * **Graph C** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original quiz containing this question can be found here: Quiz 1. Note: All Khan Academy content is available for free at www.khanacademy.org.24:T4e4,$\lim\limits_{x \to 3}g(x)$ represents the limit of $g$ as $x$ approaches $3$. We see that $g(3)=-3$, but that doesn't mean that the limit has the same value! Let's look at the graph and see if the $y$-values seem to approach a distinct value as the $x$-values approach $3$. If we approach $x=3$ from the left, the $y$-values get closer adn closer to $4$. If we approach $x=3$ from the right, the $y$-values get closer and closer to $-3$. The function does not approach the same value from both directions. [[graph 1]] **The limit $\lim\limits_{x \to 3}g(x)$ doesn't exist.** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original exercise containing this question can be found here: Estimating limit values from graphs. Note: All Khan Academy content is available for free at www.khanacademy.org.

Exam 2