How do you prove the statement lim as x approaches -1.5 for # ((9-4x^2)/(3+2x))=6# using the epsilon and delta definition?
You can't prove it since it isn't 6.
See the explanation.
We need to show that for every positive
Note first that
So, for every
# = abs(-2x-3) = abs((-4)(x+3/2)) = abs(-4)abs(x+3/2)#.
# = 4abs(x+3/2)#
We want this to be less than
If we make
Now we are ready to write the proof:
# = abs(-2x-3) = abs(-4)abs(x+3/2)#.
# = 4abs(x+3/2) < 4delta = 4(epsilon/4) = epsilon#
That is: if
So, by the definition of limit,