## Discontinuous limits

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### 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?
bebesofly
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### Re: Discontinuous limits

bebesofly wrote: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.
mathman
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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.

$f(x) \;=\;\left\{\begin{array}{ccc}a\,-\,x^2 & \text{ for }x \,<\, -1 \\ x\,-\,b & \text{ for }x \,>\, -1 \end{array}$

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?

I assume you're seeking values of a and b which make the function discontinuous at x = -1.

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

From the left: .$f(-1) \:=\:a\,-\,(-1)^2\:=\:a-1$

From the right: .$f(-1) \:=\:-1 - b$

If they are equal: .$a\,-\,1 \:=\:-1\,-\,b \qquad\qquad\Rightarrow\qquad\qquad a + b \:=\:0$

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

soroban
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