Posted by Anonymous on Saturday, September 24, 2011 at 2:54pm.
Let f be defined as follows:
h(x)=
x3 for x greater than or equal to 1
ax+b for 2<x<1
x(squared) for x less than or equal to 2
Find the values of "a" and "b" that make h(x) continous.
I'm a bit stumped on how to go about solving this one. Help would be greatly appreciated. :)

calculus  Reiny, Saturday, September 24, 2011 at 3:16pm
look at the transition points, they should be the same.
when x = 1
h(x) = x  3 = 13 = 4
h(1) = a + b
so a+b = 4
h(2) for ax+b = 2a+b
h(2) for x^2 = 4
so 2a + b = 4
a+b = 4
2a +b = 4
subtract:
3a = 8
a = 8/3,
back in a+b= 4
8/3+b = 4
b = 20/3
a = 8/3 , b = 20/3