The following limit represents the derivative of some function f at some number a.
limx→5 (2^x−32)/(x−5)

State f and a

Question

The following limit represents the derivative of some function f at some number a.
limx→5 (2^x−32)/(x−5)

State f and a

turingtest · Answer

$$\lim_{x\to5}{2^x-32\over x-5}=f'(a)$$find $f$ and $a$
is that the problem?

turingtest · Answer

$$\lim_{x\to5}{2^x-32\over x-5}=\lim_{x\to5}{2^x-2^5\over x-5}$$so what is the function?

anonymous · Answer

yes that is the question.  I don't understand how there can still be x variables in the derivative since a = 5, the x's should all be 5's?

turingtest · Answer

the definition of the derivative of a function f at a point x=a can be stated as$$f'(a)=\lim_{x\to a}{f(a)-f(x)\over a-x}$$

turingtest · Answer

all they want you to do is identify the pieces
based on the similarities between the definition and your formula, what is f?
what is a?

turingtest · Answer

you have correct that a=5, but you can't just plug in x=5 everywhere or it's not a limit anymore, it would just be zero in both numerator and denominator

anonymous · Answer

Got it, thanks!