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)=

Nina has prepared the following two-column proof below. she is given that ∠oln ≅ ∠lno and she is trying to prove that ol ≅ on. triangle oln, where angle oln is congruent to angle lno step statement reason 1 ∠oln ≅ ∠lno given 2 draw oe as a perpendicular bisector to ln by construction 3 ∠leo ≅ ∠neo transitive property of equality 4 m∠leo = 90° definition of a perpendicular bisector 5 m∠neo = 90° definition of a perpendicular bisector 6 le ≅ en definition of a perpendicular bisector 7 δole ≅ δone side-angle-side (sas) postulate 8 ol ≅ on cpctc nina made two errors in the proof. identify and correct the errors.