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 November 21st, 2009, 11:16 AM #1 Joined: Nov 2009 Posts: 2 Thanks: 0 Discontinuous limits If f(x) = a-x^2 if x<-1, and x-b if x>-1 How do I figure out the values of a and b ? Is it any values that make the f(x) value different when x is approached from the left or the right?
November 21st, 2009, 04:21 PM   #2
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Re: Discontinuous limits

Quote:
 Originally Posted by bebesofly If f(x) = a-x^2 if x<-1, and x-b if x>-1 How do I figure out the values of a and b ? Is it any values that make the f(x) value different when x is approached from the left or the right?
Your question is very unclear. At x=-1 you have from the left a-1 and from the right -1-b. For continuity a=-b. Without any more information that is as far as you can get.

November 21st, 2009, 07:14 PM   #3
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Re: Discontinuous limits

Hello, bebesofly!

As mathman pointed out, the question is not clearly stated.
We must guess the intent of the problem.

Quote:
 $f(x) \;=\;\left\{\begin{array}{ccc}a\,-\,x^2 &\text{ for }x \,=<\, -1 \\ x\,-\,b=&\text{ for }x \,=>\, -1 \end{array}=$ How do I figure out the values of $a$ and $b$ ? Is it any values that make the $f(x)$ value different when $x$ approaches -1 from the left or the right? [color=blue]I assume you're seeking values of a and b which make the function discontinuous at x = -1.[/color]

If the function is continuous at $x= -1$, then $f(-1)$ has the same value "from both sides."

From the left:[color=beige] .[/color]$f(-1) \:=\:a\,-\,(-1)^2\:=\:a-1$

From the right:[color=beige] .[/color]$f(-1) \:=\:-1 - b$

If they are equal:[color=beige] .[/color]$a\,-\,1 \:=\:-1\,-\,b \qquad\qquad\Rightarrow\qquad\qquad a + b \:=\:0$

$\text{Therefore, the function is }dis\text{continous at }x \,=\,-1\,\text{ if }\,a + b \:\neq\:0$

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