Part i:
To determine if T is continuous at 6061, we must know whether or not the left hand limit is equivalent to the right hand limit for T(6061).
The left hand limit uses the equation [tex]0.10x[/tex].
Plug in 6061.
[tex]0.10(6061)=606.10[/tex]
The right hand limit uses the equation [tex]606.10+0.18(x-6061)[/tex].
Plug in 6061.
[tex]606.10+0.18(6061-6061)=606.10[/tex]
Since the left hand limit for 6061 is equivalent to the right hand limit, the function is continuous at 6061.
Part ii:
We'll do the same steps similar to the last part of this problem. Let's find out whether or not the left and right hand limits are equal to each other.
The left hand limit uses the equation [tex]606.10+0.18(x-6061)[/tex].
Plug in 32,473.
[tex]606.10+0.18(32,473-6061)=5360.26[/tex]
The right hand limit uses the equation [tex]5360.26+0.26(x-32,473)[/tex].
Plug in 32,473
[tex]5360.26+0.26(32,473-32,473)=5360.26[/tex]
Since the left limit is equivalent to the right hand limit (once again), the piece wise function is continuous at 32,473.
Part iii:
From part i and part ii, we didn't find any discontinuities. Also, looking at the piece-wise function, I believe that there are no other discontinuities at other values for x (you might want to verify this just to make sure).
Thus, this part cannot be answered because it is not applicable.
