Use continuity to evaluate the limit. lim
x→9 16+√x/√16+x
Consider the intervals for which the numerator and the denominator are continuous.
The numerator 16+√x
is continuous on the interval Correct The denominator √16+x is continuous and nonzero on the interval

The interval for which the quotient is continuous is the intersection of the above intervals. Therefore, the quotient 16+√x/√16+x is continuous on the interval
Since x=9 is in the interval [0,∞) , then f is continuous at x=9 . Therefore, limx→9
16+√x/√16+x=f(9)=