find the constant c that makes g continuous (g in two parts)  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

find the constant c that makes g continuous (g in two parts)

Postby nona.m.nona on Mon Dec 15, 2008 2:01 pm

This is from my calculus book, but I think I only need algebra:

Find the constant c that makes g continuous on (-infinity, +infinity):

.        /
| x^2 - c^2 if x < 4
g(x) = <
| cx + 20 if x >= 4
\

(The dot above doesn't mean anything, but the first line wouldn't line up without a leading character.)

"Continous" just means that the two ends line up, right? So I just have to do:

42 - c2 = 4c + 20

16 - c2 = 4c + 20

0 = c2 + 4c + 4

0 = (c + 2)2

-2 = c

This would make the two ends meet up at (x, y) = (4, 12). Is that okay? I'm not forgetting any "calculus" stuff for this, am I?

Thanks in advance. :mrgreen:
nona.m.nona
 
Posts: 254
Joined: Sun Dec 14, 2008 11:07 pm

Sponsor

Sponsor
 

  TOPIC_SOLVED

Postby stapel_eliz on Tue Dec 16, 2008 12:32 pm

nona.m.nona wrote:This would make the two ends meet up at (x, y) = (4, 12). Is that okay? I'm not forgetting any "calculus" stuff for this, am I?

I'm not familiar with any extra, calc-specific stuff that you "should" do in addition to what you've done. And your value for "c" makes the two ends meet "in the middle", so your answer looks good to me! :D

Eliz.
User avatar
stapel_eliz
 
Posts: 1715
Joined: Mon Dec 08, 2008 4:22 pm


Return to Advanced Algebra ("pre-calculus")