### Home > PC > Chapter 5 > Lesson 5.2.3 > Problem5-78

5-78.

Let $g\left(x\right)$ be the function $\frac { 2 ^ { x } - 2 } { 3 ^ { x } - 3 }$.

1. Below is a table of values for $g\left(x\right)$ for $x$ near $1$. Estimate $\lim\limits _ { x \rightarrow 1 } g(x)$.

Check at $x = 0.9999$ and at $x = 1.0001$. What do you notice?

x

g(x)

$0.9$

$0.4291$

$0.95$

$0.4249$

$0.99$

$0.4215$

$0.999$

$0.4207$

$0.9999$

$0.42063$

x

g(x)

$1.1$

$0.4120$

$1.05$

$0.4164$

$1.01$

$0.4198$

$1.001$

$0.42053$

$1.0001$

$0.42061$

2. Use a graph to decide if you can get a better estimate of the limit for $g\left(x\right)$ as $x → 1$.