Find lim x->2 (f(x^2+5) - f(9))/(x-2), knowing that f'(x) = 1/x and f(2) = 9.
I am not sure how to solve this. I suppose f(x) = ln(x), but I don't think that helps me, since the textbook hasn't introduced natural logarithm yet, and from what has been covered so far, I am guessing that it can be solved some other way without this knowledge. Evaluating as is obviously generates a zero denominator.
And thats all I can say, I am completely stumped as to where to begin?
hmm, it is in the 'Challenging Problems' section of the chapter, but there has been no coverage of Lhopital's rule, and exponential and logarithmic functions aren't covered 'til CH 4. FYI, it is problem 2(a), challenging problems at end of Chapter 2 of Calculus 3/E (Robert A. Adams), if anyone has access to this text.