Question

use the table of values of f to estimate the limit. let f(x) = x^2 + 8x - 2, find lim(x→2) f(x).

Explanation:

Step1: Recall the concept of limit

The limit of a function $f(x)$ as $x$ approaches $a$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both the left - hand side and the right - hand side.

Step2: Analyze the function $f(x)=x^{2}+8x - 2$

We can also find the limit by direct substitution since $f(x)$ is a polynomial function and is continuous everywhere. Substitute $x = 2$ into $f(x)$:
\[

$$\begin{align*} f(2)&=2^{2}+8\times2 - 2\\ &=4 + 16-2\\ &=18 \end{align*}$$

\]
As $x$ approaches $2$ from the left - hand side ($x = 1.9,1.99,1.999$) and the right - hand side ($x=2.001,2.01,2.1$), the values of $f(x)$ should approach the value of $f(2)$.

Answer:

C.

$$\begin{array}{|c|c|c|c|c|c|c|}\hline x&1.9&1.99&1.999&2.001&2.01&2.1\\\hline f(x)&16.810&17.880&17.988&18.012&18.120&19.210\end{array}$$

; limit = $18.0$