Question

Can someone please explain how to do these?

Answer 1

First question answer: The limit is 69

Second question answer: The limit is 5

Explanation:

For the first limit, plug in
`x=8` in the expression
`(9x-3)`, that's the answer for linear equations and limits.

So we have:

`9x-3\\9(8)-3\\72-3\\69`

The answer is 69

For the second limit, if we do same thing as the first, we will get division by 0. Also indeterminate form, 0 divided by 0. Thus we would think that the limit does not exist. But if we do some algebra, we can easily simplify it and thus plug in the value
`x=1` into the simplified expression to get the correct answer. Shown below:

`(x^2+8x-9)/(x^2-1)\\((x+9)(x-1))/((x-1)(x+1))\\(x+9)/(x+1)`

Now putting 1 in
`x` gives us the limit:

`(x+9)/(x+1)\\(1+9)/(1+1)=(10)/(2)=5`

So the answer is 5