2 Cal 1 problems cant figure out

1. Feb 5, 2005

ElectricMile

1) the given function is defined for x>0 except for x=2. Find the value to be assigned to f(2), if any, to guarantee that f is continuous at 2.

f( x ) = sin(pi x) / (x-2)

cant figure out how to change the equation so i can plug 2 in, i think im loking right past it, tried multiplying by x-2, didnt work

2) For what value of the constants a and b is the function f continuous for all x

f(x) = ( (ax-4)/(x-2) x not equal to 2
|
| b x = 2
(

i know b is equal to to, but cant figure out how to change the first equation to find a.

2. Feb 5, 2005

christinono

For the first question, do you mean "to guarantee that f is discontinuous at 2"? If that's what you mean, just substitute x=2 into the equation. You should be able to see right away that it cannot exist at that point. Hint: look at the denominator...

3. Feb 5, 2005

Townsend

For number 1 you have a removable discontinuity. You don't actually change the equation you must make f(x) into a piecewise defined function so that when x=2 the definition of f(x) is such that it is defined and so that it is continuous at x=2. So you would want to know the limit of f(x) as x approached 2. that is a 0/0 so you need to figure out what to do from here.

Good luck

Last edited: Feb 5, 2005
4. Feb 5, 2005

Townsend

for number 2, all I see is an a in the expression you gave. I would need to know where the b is to figure that one out. Maybe you could rewrite it and make sure it is exaclty as it should be? Then I might be able to help you some more.

Regards

5. Feb 5, 2005

stunner5000pt

can't you jsut use L'Hopital's rule for the first part

6. Feb 5, 2005

Townsend

Yeah but he was suppose to figure that one out on his own......