Question

Complete the table and estimate the limit

Answer 1

Answer:

$\lim_{x \to -7} \frac{\sqrt{2-x}-3 }{x+7}=-\frac{1}{6}$ or $-0.1\bar6$

Step-by-step explanation:

We want to evaluate;

$\lim_{x \to -7} \frac{\sqrt{2-x}-3 }{x+7}$

by the intuitive approach.

$f(-7.1)=-0.1662$

$f(-7.01)=-0.1666$

$f(-7.001)=-0.1667$

$f(-6.999)=-0.1667$

$f(-6.99)=-0.1667$

$f(-6.9)=-0.1671$

As we are getting closer and closer to $-7$ from both sides, the function is approaching $-\frac{1}{6}$