If lim f (x) x →5 = 2 and lim g (x) x → 5= -6 which of these limits exist?

E

Step-by-step explanation:

So we already know that:

So, go through each of the choices and see which ones are correct.

I)

We have:

This is the same as saying:

And since we already know the values:

So, the limit does indeed exist.

II)

We have:

This is the same as:

The bottom right one is just 6. Simplify:

Substitute the values we know:

This is a value over zero. Unlike the indeterminate form 0/0, this limit does not exist.

III)

We have:

Again, this is the same as:

Substitute in the values we know:

The limit does exist and it is 0.

So, the limits of only I and III exist.

The correct answer is E.

i need the options

step-by-step explanation: