Evaluate the limit and explain. What is the limit as x approaches 2 from the right side? (+)

Question

Let f(x)=x^3 when x is less than or equal to 2

and x-2 when x is greater than 2 (Piecewise function)

What is the limit of x approaching 2 from the right side? Explain.

 

I'm pretty sure it's 0 because the 2nd part of the function (x-2) is for when x is greater than 2, so the first is unnecessary.

Can someone confirm and please explain? 

Answer 1

Since we want the limit approaching x=2 from the right, we will evaluate f(x) when x≥2.

 

f(2) = 2³ = 8

f(2.0001) = 2.0001 - 2 = 0.0001

f(3) = 3 - 2 = 1

f(4) = 4 - 2 = 2

f(5) = 5 - 2 = 3

 

 

If we work backwards, as x approaches x=2 from the right side, f(x) gets closer to zero