Question

Consider the following limit. Precalculus

lim
x→2 x − 2/
x2 − 16x + 28

Complete the table. (Round your answers to four decimal places.)
x 1.9 1.99 1.999 2 2.001 2.01 2.1
f(x)


?

Use the result to estimate the limit.

Answer 1

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

$\displaystyle \lim_{x \to2} \: \: \small\frac{x - 2}{ {x}^{2 } - 16x + 28 }$

$\displaystyle \lim_{x \to2} \: \: \small \bigg(\frac{x - 2}{ {x}^{2 } - 14x - 2x+ 28 } \bigg)$

$\displaystyle \lim_{x \to2} \: \: \small \bigg(\frac{x - 2}{ x( x- 14) - 2(x - 14) } \bigg)$

$\displaystyle \lim_{x \to2} \: \: \small \bigg(\frac{ \cancel{(x - 2)}}{ \cancel{(x - 2)}( x- 14) } \bigg)$

$\displaystyle \lim_{x \to2} \: \: \small \bigg(\frac{1}{ ( x- 14) } \bigg)$

$\sf = \frac{1}{2 - 14}$

$\sf = \frac{ - 1}{12}$