(i) To show that a piecewise function is continuous at a point, we need to show that the left hand and right hand limit "agree" with each other. In other words, we want:
![\lim_{x\to 6061^-} T(x) = \lim_{x \to 6061^+} T(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%206061%5E-%7D%20T%28x%29%20%3D%20%5Clim_%7Bx%20%5Cto%206061%5E%2B%7D%20T%28x%29)
Now, since we're given the constraints and the equation of each constraint, we notice that 6061^+ is a number that is slightly bigger than 6061. So we use the second equation. Do you see why?
In much the same way, 6061^- is a number that is slightly smaller than 6061. So we use the first equation. Again, do you see why? (Hint: look at the conditions on x for each equation).
So finally, computing each limit means just "plugging" 6061 into their respective equations. That is:
![\lim_{x \to 6061^-} T(x) = 0.10\times 6061 = 606.1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206061%5E-%7D%20T%28x%29%20%3D%200.10%5Ctimes%206061%20%3D%20606.1)
![\lim_{x \to 6061^+} T(x) = 606.1 + 0.18(6061 - 6061) = 606.1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206061%5E%2B%7D%20T%28x%29%20%3D%20606.1%20%2B%200.18%286061%20-%206061%29%20%3D%20606.1)
Since your limits match, we say that, at the point x = 6061, T(x) IS continuous.
(ii) Repeat the process above with x = 32473.
(iii) Find a point of discontinuity just means your right hand and left hand limits do not match -- I'm not an economist, so I may not be of much help with the latter part of the question!
Answer:
The missing angle is 50 degrees.
Answer:
60%
Step-by-step explanation:
The 2100 people surveyed said they would buy it again, meaning they were satisfied. A total of 3500 people were surveyed.
So 2100 / 3500 = 60%
please give thanks :)
Answer:
Step-by-step Three customers have accounts owing money. The table shows the account balances.
Which customer owes the least amount of money?
Customer Balance
M. Palmer –$56.72
B. Leftwich –$74.19
R. Jordan –$54.31
dose anybody know
:
Answer:
x=40
Step-by-step explanation:
solving for x: 4x= 180-20
x= 160/4 =40