00:01
In this question, we are told that f prime is continuous, f of 1 is 0, and f prime of 1 equals to 7.
00:08
And we are asked to find the limit of f of 1 plus 2x plus 5x over x as x goes to 0.
00:18
First of all, note that if you plug in x equals 0, you are going to get f of 1 plus f of 1 divided by 0.
00:30
And recall that f of 1 is 0, so it's going to be 0 or 0.
00:34
So that's an indeterminate form.
00:38
And since it's an indeterminate form 0 over 0, we can use the lopital's rule.
00:46
And by the lopetals rule, the original limit equals to the limit of the ratio of the derivatives.
00:56
So what we're going to do is we will differentiate the numerator and the denominator separately.
01:01
The key word here is separately.
01:04
The derivative of the numerator is the derivative of f of 1 plus 2...
