Use continuity to evaluate the limit. 40+ lim 29 40+x Consider the intervals for which the numerator and the denominator are continuous. The numerator 40+ is contintuous on the interval The denominator 40+ is continuous and nonzero on the interval The interval for which the quotient is continuous is the intersection of the above intervals. is continuous on the interval Therefore, the quotient 40+ 40+x Since = 9 is in the interval [0, ), then f is continuous at x = 9. Therefore, 40+ lim = f(9) = 19 40+x