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:
limx->a- f(x) = limx->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:
limx->-3- (5x3+162+10x+21)/x+3 = limx->-3+ f(x)=-3x2+2x+a
If you need help with these limits, I'll be checking in.
Lin S.how to find the answer while the first limit does not exist?