Find Values of Alpha and Beta That Make F Continuous

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Find the values of a and b that make f continuous everywhere

• Thread starter badatmaths
• Start date Sep 12, 2010

Homework Statement

Find the values of a and b that make f continuous everywhere. (Enter your answers as fractions.)

Homework Equations

The Attempt at a Solution

lim x->2 (x²-4)/(x-2) = 0

lim x->2 4a - 2b +5
lim x->3 9a - 3b +5

lim x->3 12 - a + b

4a - 2b + 5 = 0
4a - 2b = -5

9a - 3b +5 = 12 - a + b
10a - 4b = 7

4a - 2b = -5
a = 2.5b/4

10(2.5b/4) - 4b = 7
6.25b - 4b = 7
2.25b = 7
b = 28/9

I'm obviously missing something because I've been screwing around with this problem for well over an hour already and I haven't been able to solve it. I need to get this done by tomorrow morning so any help is appreciated.

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Answers and Replies

You've got the right method, but there's a problem with the first step. lim x->2 (x^2-4)/(x-2) isn't zero.

You've got the right method, but there's a problem with the first step. lim x->2 (x^2-4)/(x-2) isn't zero.

I'm really not sure what to do if x->2 for the first equation is undefined...

I'm really not sure what to do if x->2 for the first equation is undefined...

Try and factor the numerator and cancel the factor which is going to zero.

Try and factor the numerator and cancel the factor which is going to zero.

(x+2)(x-2)/(x-2)
(x+2)
x->2 = 4

That would mean that...

4a - 2b + 5 = 4
4a - 2b = -1
4a = 1/2b
a = 1/8b

But plugging that into 10a - 4b = 7 gives me...

10(1/8b) - 4b = 7
(5/4)b - 4b = 7
(-11/4)b = 7
b = -28/11

...Okay, that isn't right...I did this problem 3 different times and came up with a new answer each time.

(x+2)(x-2)/(x-2)
(x+2)
x->2 = 4

That would mean that...

4a - 2b + 5 = 4
4a - 2b = -1
4a = 1/2b
a = 1/8b

But plugging that into 10a - 4b = 7 gives me...

10(1/8b) - 4b = 7
(5/4)b - 4b = 7
(-11/4)b = 7
b = -28/11

...Okay, that isn't right...I did this problem 3 different times and came up with a new answer each time.

You are goofing up your algebra. 4a-2b=(-1) doesn't lead to 4a=(1/2)b. What are you doing?

You are goofing up your algebra. 4a-2b=(-1) doesn't lead to 4a=(1/2)b. What are you doing?

I'm going to blame it on the embarrassingly long amount of time I've been looking at this problem. I just solved, finally. Thanks a lot! I really appreciate it!

I'm going to blame it on the embarrassingly long amount of time I've been looking at this problem. I just solved, finally. Thanks a lot! I really appreciate it!

Staring at a problem for too long does make this stuff happen. Glad you got it.

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