Question

Complete the table and estimate the limit

Answer 1

`\lim_(x \to -7) (√(2-x)-3 )/(x+7)=-(1)/(6)` or
`-0.1\bar6`

Explanation:

We want to evaluate;

`\lim_(x \to -7) (√(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
`-(1)/(6)`