Let f(x) = 5, if x > 1 f(x) = 2, if x < 1 f(x) = undefined for x = 1 Find the following one sided limit: lim𝑥→1−𝑓(𝑥)

Question

Options:

1. 1
2. limit does not exist
3. 6
4. 2

Answer 1

f(x) = 5, if x > 1 f(x) = 2, if x < 1 f(x) = undefined for x = 1

 lim_𝑥→1−𝑓(𝑥)= lim_𝑥→1^-=2

Answer 2

This is a piece-wise function, and easier to read as:

f(x) = 2 for x < 1 (this is the horizontal line y = 2 with an open dot at (1, 2) and continuing left)

f(x) = und. for x = 1

f(x) = 5 for 1 < x (this is the horizontal line y = 5 with an open dot at (1, 5) and continuing right)

A: As we approach x = 1 from the left, the limit looks like it equals 2. The function value does not have to exist for the limit to work. Think of shooting an arrow from a bow and seeing where it will land.

See graph at: https://www.desmos.com/calculator/h3hfsta9lo