Find the limit as x approaches 1.
Plug in 1 into x.
This come out to being indeterminate or 0/0.
So taking the rule:
Step 3) Final Answer is 2.
Anyhow, I see the pattern of how the answer came about, but I don't understand the reasoning behind it. Well, I understand differintiation part. However. where did the fraction inside of the fraction come from in Step 2? Why did the square root in Step 2 get moved to the numerator in the final answer?
What Plato's saying is, you probably messed up the arithmetic or something when you obtained an answer of 3 (did you forget the square root sign?). Also, what is wrong with the answer being indeterminate and 2? 0/0 is indeterminate because it could equal anything; that's why we use other techniques (L'Hopital's rule or plain algebra) to determine the limit, which is 2.
Let's return back to the original solution, using L'Hopital's rule. Step 2 in your original solution should be easy if you know how to find derivatives. To get to step 3, you should also know that.
Went back and edited the post, it came out to 3, Plato was right. However, the book says 2. If differentiated using L Hospital's rule, then it comes out to 2. The book is from a major bookstore. I guess it's wrong.
Plugging in 1 gets 3 for the limit.