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?

## Answer This Question

## Related Questions

- Calculus - Find all values of a, B so that the function f(x)=1 if x>3, f(x)=...
- calculus - Find the values of a and b that make f continuous everywhere. (Enter ...
- Calculus - Use the given derivative to find all critical points of 'f' and at ...
- calculus - Find the values of a and b that make f continuous everywhere. (Enter ...
- Calculus - Use the given derivative to find all critical points of 'f' and at ...
- calculus - For what values of a and b that make the function f continuous ...
- Calculus - Let If f(x) is a function which is continuous everywhere, then we ...
- calculus - Let h(x) = ( x2 + 2 if x > 2 ��mx if x 2 (a) Find ...
- Calculus - COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on ...
- Calculus - COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on ...

More Related Questions