Question

Estimate the following limit by substituting smaller and smaller values of h. (5+h)^3-125/h

Answer 1

I was just confused how to begin this problem. Would I plug in 0.001 for h?

Answer 2

Yeah so try any number for h and plug it into the formula

Answer 3

You'll notice that the first term (5+h)^3 gets closer and closer to 125
The second term will keep getting larger and larger so its going to infinity as h gets smaller and smaller

Answer 4

So would the answer be zero because it is a smaller number over a large number?

Answer 5

Are you trying to find the limit?

Answer 6

So the limit as h->0 from the left side(negative numbers) the limit is infinity
The limit as h approaches 0 from the right side(positive side) the limit is negative infinity
But the limit at 0 does not exist because the limit of the left side does not equal the limit of the right side

Answer 7

So if you were to look at a graph the line coming in from the left side would be going up and the line coming from the right side would be going down and they would never met or actually touch 0