Expert: Paul Klarreich - 4/4/2008

Question
Figure 11.1 is the mathematical equation that was listed below it.... f(x) = {c2 - x2 if x<0 OVER ccosx if x> or = 0

Given Figure 11.1 (as seen above), find a value for c so that f(x) is continuous for all x.

Answer
Questioner:   Andrea
Category:  Calculus
Private:  No
 
Subject:  Calculus 1
Question:  Figure 11.1 is the mathematical equation that was listed below it.... f(x) = {c2 - x2 if x<0 OVER ccosx if x> or = 0

Given Figure 11.1 (as seen above),

>> I still don't see any Figure 11.1

find a value for c so that f(x) is continuous for all x.
.....................................  
Hi, Andrea,

If you want to send me questions, here is what you must do.

Click BROWSE PAST ANSWERS on the site and read a couple of dozen of them.  You will see how mathematical expressions are written on the computer.  Then you will be able to send your questions in a form that I can understand.

Here is what you wrote:


f(x) = {  c2 - x2
         -------- if  x < 0
          ccos x

         if x> or = 0

Here is what I think you meant to write:
      {  c^2 - x^2
f(x) = { ----------,  if  x < 0
      {      c
      {
      {   cos x   ,  if  x >= 0

To answer your question, you want  lim[x->0] f(x) on each side.

On the left side, as x -> 0, the limit is  c^2/c = c.

On the right side, as x -> 0, the limit is  cos 0 = 1.

So you must have  c = 1.

So feel free to send me questions, but remember that my job is to answer them, not to figure out what they are.  If you send me gibberish, that's what you will get back.