# Thread: limit of 2^x - 32 / x-5

1. ## limit of 2^x - 32 / x-5

i can't figure it out for some reason it's weird!

each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.

limit as x-->5

2^x - 32 / x-5

i keep trying but i can't get it right!

if it helps i know the answer in the back of the book says
f(x)=2^x, a=5

please and thank you!

2. Originally Posted by jayjay60
i can't figure it out for some reason it's weird!

each limit represents the derivative of some function "f" at some number "a". state such an "f" and "a" in each case.

limit as x-->5

2^x - 32 / x-5

i keep trying but i can't get it right!!!!
if it helps i know the answer in the back of the book says
f(x)=2^x, a=5

please and thank you!
are you familiar with the difference quotient?

$\displaystyle f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}$

match it up ...

$\displaystyle f'(5) = \lim_{x \to 5} \frac{f(x) - f(5)}{x-5}$

$\displaystyle f'(5) = \lim_{x \to 5} \frac{2^x - 2^5}{x-5}$

3. yes, well i can't understand how f(x)=2^x, a=5 is the answer though? :<

4. oh gosh. i hate when they're so simple it's easy to overlook!!! thank you so much.

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### the limit below represents the derivative of some function f(x) at some number a

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