# Math Help - Limits

1. ## Limits

for the function g(x) = rx^2 if x<or=12 and 4x + r if x>12, determine a value for r that makes g(x) continous

What formula do you use to get r

2. Originally Posted by aaasssaaa
for the function g(x) = rx^2 if x<or=12 and 4x + r if x>12, determine a value for r that makes g(x) continous

What formula do you use to get r
ok, so i'm only about 98% sure that this is the way to go about a solution. obviously we'll have a problem at x = 12. Now for the function to be continuous at this point, the right hand limit at the point, must be equal to the left hand limit at the point. the left hand limit comes from tracing along the rx^2 function, while the left hand limit comes from tracing along the 4x + r function. thus we want to make sure that both functions are the same at this point. and so we want:

rx^2 = 4x + r at x = 12
=> r(12^2) = 4(12) + r
=> 144r = 48 + r
=> r = 48/143
this value of r should make the functions continuous. ploting the functions using some graphing utility vindicates this solution

3. Originally Posted by aaasssaaa
for the function g(x) = rx^2 if x<or=12 and 4x + r if x>12, determine a value for r that makes g(x) continous

What formula do you use to get r
g is continous for x>12 and x<12.
The only possible point is x=12.

We need that,
lim right (x=12) g(x) = lim left (x=12) g(x) = g(12)

Thus,
4(12)+r=r(12)^2=r(12)^2

Solve,
48+r=144r