Posted by **Anonymous** on Sunday, March 7, 2010 at 3:34pm.

Given

F(x) = ax+3, x>5

8 , x=5

x^2 + bx + a, x<5

Find a and b so that f(x) is continuous everywhere.

- calculus -
**MathMate**, Sunday, March 7, 2010 at 7:51pm
For x to be continuous everywhere,

Lim x→5 =8 .....(1)

Lim x→5- =8,.....(2), and

Lim x→5+ =8,.....(3)

(1) is satisfied by setting

F(5)=8

(2) can be satisfied by setting

F(5)=ax+3 = 8

and solving for a.

(3) can be satisfied by setting

F(5) = x^2 + bx + a = 8

and solving for b using the previously solved value of a.

Can you take it from here?

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