Question

Find the limit. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

lim x→107 x -107 /√x+14 - 11
f(x)= (Type an integer.)

Answer 1

To find the limit of the function f(x) = (x - 107) / (√x + 14 - 11) as x approaches 107, substitute 107 for x and simplify. The limit is 0.

Step-by-step explanation:

To find the limit of the function f(x) = (x - 107) / (√x + 14 - 11) as x approaches 107, we can substitute 107 for x in the function and simplify. This gives us f(107) = (107 - 107) / (√107 + 14 - 11) = 0 / (√107 + 14 - 11) = 0 / (√107 + 3).

Since the denominator approaches √107 + 3 = 10 + 3 = 13 as x approaches 107, the limit of the function f(x) as x approaches 107 is 0 / 13 = 0.