How do you prove that the limit of #f(x) =2x-3# as x approaches 5 is 7 using the epsilon delta proof?
2 Answers
The function
To prove it using the limit definition consider the value:
For
Given any
which proves the limit.
Please see below.
Explanation:
Given
Now if
# = 2 abs(x-5)#
# < 2delta# #" "# (since#abs(x-5) < delta# )# = 2(epsilon/2)
# = epsilon#
That is: if