Eric C. answered • 02/05/20

Math and Physics teacher with over twenty years of teaching experience

A function f is continuous at the point x = a if the limits of the function as it approaches the point from the right and the left are equal. In equation form this looks like:

lim_{x->a- }f(x) = lim_{x->a+ }f(x)

In this case the point we are looking at is x = -3. The function we are given is a piecewise function with a different formula on either side of x = -3. Thus, we must be careful to use the correct formula when taking the limits from the left and right. Plugging in the correct formulas gives:

lim_{x->-3}^{- }_{ }(5x^{3}+16^{2}+10x+21)/x+3 = lim_{x->-3}^{+}_{ } f(x)=-3x^{2}+2x+a

If you need help with these limits, I'll be checking in.

Eric C.

02/05/20

Lin S.

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