Question

Find the limit of the following functions using the tabular method.

1. lim    x2+x-6x+3/ x+3

𝑥→−3

1. lim x2-2x+3/ x+1   

𝑥→−1

Answer 1

1.

$$\lim_{x\rightarrow-3} \frac{x^2+x-6x+3}{ x+3}\\$$

Let $f(x) = \frac{x^2+x-6x+3}{ x+3}\\$

$\def\arraystretch{1.5} \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & -3.2 & -3.19 &-3.09 &-3.01 &-2.99 &-2.9 &-2.89&-2.8 \\ \hline f(x) &-146.2 & -153.29 &-311.09&-2711.01&2689.01&259.1&234.56&124.2\\ \hline \end{array}$

The limit of the function as x approaches -1 does not exist, since the value of x from the left approaches smaller negative value and the the value from the right approaches large positive value.

2.

$$\lim_{x \rightarrow -1} \frac{x^2-2x+3}{x+1}$$

Let $f(x) = \frac{x^2-2x+3}{x+1}$

$\def\arraystretch{1.5} \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & -1.2 & -1.11&-1.1 &-1.01 &-0.99 &-0.9 &-0.89&-0.8 \\ \hline f(x) &-34.2& -58.66 &-64.1&-604.01&596.01&56.1&50.65&26.2\\ \hline \end{array}$

The limit of the function as x approaches -1 does not exist, since the value of x from the left approaches smaller negative value and the the value from the right approaches large positive value.