Question

Piecewise defined function
h(x) = x if x < 0
h(x) = x^2 if 0 < x <=2
h(x) = 8 - x if x >2

Does the limit of h(x) as x approaches 0+ exist? in this case x could satisfy 0 < x <=2 or x > 2 so which one would I use?

Answer 1

Use the middle one. We only care about how the function behaves as it approaches 0 from the right (i.e., for positive values of x). The other two pieces are irrelevant for this limit.

Answer 2

What about for the limit as x approaches 2-? Would I just use the the middle one as well?

Answer 3

If x approaches 2 from the left , then again, the middle one is the only relevant piece

Answer 4

You should get 0 for the first limit and and 4 for the second.

Answer 5

ok and would the limit as x approaches 0 be 0?

Answer 6

yep. the left and right hand limits agree.

Answer 7

Thanks for the help!

Answer 8

np