Question

how do i get the answer for this limit limit x to 0 (4^2x-1)
without using direct substitution
my work so far is

limit x to 0= (4^2x-1)
= (4^2x/4^-1)

is it correct?

Answer 1

I don't see the problem with this limit question other than your notation.

I will assume you meant:
lim 4^(2x -1) , as x ---> 0

Since you don't want to use substitution, which is always my first step, you could look at the graph of y = 4^(2x-1) and observe what it does at the y-axis.
http://www.wolframalpha.com/input/?i=y+%3D+4%5E(2x-1)+from+x%3D+-.5+to+.5

Notice the y-intercept is .25 or 1/4 and the graph is continuous.

my work:
lim 4^(2x -1) , as x ---> 0
= lim 4^(0-1)
= 4^-1
= 1/4