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 $\lim_{x
ightarrow a}f(x)$ is the value that $f(x)$ approaches as $x$ gets closer and closer to $a$. We can estimate it by looking at the values of $f(x)$ as $x$ approaches 2 from the left - hand side ($x = 1.9,1.99,1.999$) and the right - hand side ($x=2.001,2.01,2.1$).

Step2: Calculate $f(x)=x^{2}+8x - 2$ for each $x$ value

For $x = 1.9$:
$f(1.9)=(1.9)^{2}+8\times1.9 - 2=3.61+15.2 - 2=16.81$
For $x = 1.99$:
$f(1.99)=(1.99)^{2}+8\times1.99 - 2=3.9601 + 15.92-2=17.8801\approx17.88$
For $x = 1.999$:
$f(1.999)=(1.999)^{2}+8\times1.999 - 2=3.996001+15.992 - 2=17.988001\approx17.988$
For $x = 2.001$:
$f(2.001)=(2.001)^{2}+8\times2.001 - 2=4.004001+16.008 - 2=18.012001\approx18.012$
For $x = 2.01$:
$f(2.01)=(2.01)^{2}+8\times2.01 - 2=4.0401+16.08 - 2=18.1201\approx18.12$
For $x = 2.1$:
$f(2.1)=(2.1)^{2}+8\times2.1 - 2=4.41+16.8 - 2=19.21$
As $x$ approaches 2 from both the left - hand side and the right - hand side, $f(x)$ approaches 18.

Answer:

B. 18.0