# How do you find #lim (x+1)^(3/2)-x^(3/2)# as #x->oo#?

##### 1 Answer

#### Explanation:

So we have

We can see that this function is continuous when

Remember that when a function is continuous at

So let's substitute

Now how do we solve that?

Well, let's use logic here.

If there is this really,really large number, and we are raising it to a power greater than one, will get an answer even greater than what we started with. Also, this function will give a positive value for any

Therefore, our function will get undoubtedly large as

So you can say that

We can even look at the graph of our function.

graph{(x+1)^(3/2)-x^(3/2) [-10, 10, -5, 5]}

Even though the rate that this is increasing is decreasing, there is no limit of how much the