Estimating Limit values from graphs
There’s a difference between the value a function is approaching — what we call the limit— and the value of the function itself
lim f(x) f(0) This is not always the case x -> 0
Remember just because a function is undefined for some x-value doesn’t mean there’s no limit
And on the flip side just because the function exists for a specific value it does not mean that the limit exists
Unbound Limits
When limit on both sides does not approach a finite number yet approaches infinity People often consider these limit to DNE (does not exist), although these limits could also be referred to as Unbound Limits
eg:
lim x -> 0
As you can tell if you plug in a value closer to 0 the value of the limit just keeps on increasing never reaching an end therefore this would be considered an unbounded limit / the limit DNE