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?
2 Answers
You can't.
Explanation:
You can't prove it since it isn't 6.
See the explanation.
Explanation:
Preliminary analysis
We need to show that for every positive
Note first that
For every
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:
Proof
Given
Now if
# = 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,