Question

Are there 3 examples of when a limit does not exist?

Answer 1

1) jump discontinuity
ie when f(x) approaches a different number from the right side of c than it approaches from the left side of c
2) vertical asymptotes
example limit as x approaches pi/2 of tanx
3) limit as x approaches 0 of sin (1/x) because it oscillates between two fixed values as x approaches c

Answer 2

ok here is a dumb question
limit as x approaches 2 of (1/(x-2)^2)

Answer 3

isn't that limit +infinity

Answer 4

@zepdrix @SolomonZelman

Answer 5

I would say that it is a limit that is equal to infinity.

Answer 6

I mean the last limit you posted.

Answer 7

Approaches infinity from the left and right,
so the left-sided and right-sided limits agree?

Yah positive infinity :)

Answer 8

so for the last one the limit does exist