1. anonymous

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2. ChillOut

we need to evaluate the function at x=3. Since they are both polynomials, they should be continuous for x<3 and x>3. What we have to do now is to find both sides limits

3. ChillOut

$\lim_{x \rightarrow 3^{-}}f(x)$and $\lim_{x \rightarrow 3^{+}}f(x)$

4. anonymous

my choices is a yes o no question. I think it is continuous. am I right?

5. Owlcoffee

By definition, continuity of a function is defined by: $f:f(x)cont.(x=a) =>\lim_{x \rightarrow a}f(x)=f(a)$

6. anonymous

its continuous? am I right.

7. ChillOut

Yes. But you will have to learn it, eventually. You can only prove it's continuous by using limits.

8. ChillOut

$\lim_{x \rightarrow 3^{-}}→f(x) \lim_{x \rightarrow 3} 5x+1 = 16$and$\lim_{x \rightarrow 3^{+}}→f(x) \lim_{x \rightarrow 3} x²+7 = 16$

9. ChillOut

Wrong usage pf an arrow there. Don't mind it. it's meant to be between "f(x)" and "lim"