Answer:
[tex]\lim_{x \to -7} \frac{\sqrt{2-x}-3 }{x+7}=-\frac{1}{6}[/tex] or [tex]-0.1\bar6[/tex]
Step-by-step explanation:
We want to evaluate;
[tex]\lim_{x \to -7} \frac{\sqrt{2-x}-3 }{x+7}[/tex]
by the intuitive approach.
[tex]f(-7.1)=-0.1662[/tex]
[tex]f(-7.01)=-0.1666[/tex]
[tex]f(-7.001)=-0.1667[/tex]
[tex]f(-6.999)=-0.1667[/tex]
[tex]f(-6.99)=-0.1667[/tex]
[tex]f(-6.9)=-0.1671[/tex]
As we are getting closer and closer to [tex]-7[/tex] from both sides, the function is approaching [tex]-\frac{1}{6}[/tex]
