The limit as x approaches 0 of ((4^x)-1)/x
The limit above represents the derivative of some function f(x) at some number a. Find f and a.
Use L'Hopital's rule
lim= 4^x ln4 /1= ln(4)
so then what does f equal and what does a equal
To find the function f(x) and the number a where the given limit represents the derivative, we can use the definition of the derivative.
The derivative of a function f(x) at a number a is defined as:
f'(a) = lim (h -> 0) [(f(a + h) - f(a)) / h]
In this case, we have the limit:
lim (x -> 0) ((4^x) - 1) / x
Comparing this to the definition of the derivative, we can see that f(x) = 4^x, and a = 0.
Therefore, the function f(x) is f(x) = 4^x, and the number where the given limit represents the derivative is a = 0.