Answer:
[tex]lim_{x \to 0} f(x) = \sqrt{10}[/tex]
Step-by-step explanation:
We know that:
[tex]\sqrt{10 -7*x^2} \leq f(x) \leq \sqrt{10 -x^2}[/tex]
in the range, then we can write:
[tex]\lim_{x \to 0} \sqrt{10 -7*x^2} \leq \lim_{x \to 0} f(x) \leq \lim_{x \to 0} \sqrt{10 -x^2}[/tex]
Now we can just take the two extreme limits to get:
[tex]\sqrt{10 -7*0^2} \leq \lim_{x \to 0} f(x) \leq \sqrt{10 -0^2}[/tex]
Then we have:
[tex]\sqrt{10 } \leq \lim_{x \to 0} f(x) \leq \sqrt{10}\\\\\lim_{x \to 0} f(x) = \sqrt{10}[/tex]
