Question

Find the indicated limit, if it exists.

Limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5.
CHOICES:
A. 0
B. 8
C. 3
D. The limit does not exist
(I think it might be 3 but i also got a 40% on this test the first time I took it so)

Answer 1

the limit is the y value that the graph approaches from both sides as x approaches the target limit

it they approach different values from the left and right sides, the limit does not exist

we want to find the limit as x approaches 5

we are given that f(x)=5-x for x<5 and f(5)=8 and f(x)=x+3 for x>5

evaluate them all for f(5)
f(x)=5-x
f(5)=5-5
f(5)=0

f(5)=8

f(x)=x+3
f(5)=5+3
f(5)=8

it approaches 0 and 8 from both sides
the limit doesn't exist
D