(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:
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:
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!
Use distrubutive property <em>a(b + c) = ab + ac</em>
6(5r - 4) - 2(r - 7s - 3)
= (6)(5r) + (6)(-4) + (-2)(r) + (-2)(-7s) + (-2)(-3)
= 30r - 24 - 2r + 14s + 6
= (30r - 2r) + 14s + (-24 + 6)
<h3>= 28r + 14s - 18</h3>
I think this system is consistent and dependent
Answer:
1/-2 is the slope
Step-by-step explanation:
1/3= .3333333
.3333333 x 5= 1.6666666
1.66666+ 7(5)= 1.66666 +35
36.666666