Use the Epsilon-Delta definition to prove the limit is L.
lim (4x+9)=21
x-> 3
![]() |
Use the Epsilon-Delta definition to prove the limit is L.
lim (4x+9)=21
x-> 3
We must show that given any positive number, we can find another
positive numbersuch that
satisifies
... [1]
Whenever x satisfies... [2].
To find, we can rewrite [1] as
or
or... [/3]
We must chooseso that [3] is satisfied whenever [2]
is satisfied. So we take.
Now, can you see that the last step and finish?
4(E/4) = EQuote:
Originally Posted by galactus
Is that the last step? Thanks for your help! You are awesome, galactus!
To prove this choice works for, suppose that x satisfies [2].
Since we are letting, it follows from [2]
that x satisfies
Therefore, [3] is satisfied since it is just the right hand inequality in
This proves that
All times are GMT -7. The time now is 09:32 PM. |