Let f(x) = 2 Domain: x less than or equal to -1

= ax+b Domain: -1 less than x or less than 3

= -2 Domain: x greater or equal to 3

Find a and b such that f is continuous.

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- Jul 27th 2006, 11:06 AMNimmyCalculus I Homework Help
Let f(x) = 2 Domain: x less than or equal to -1

= ax+b Domain: -1 less than x or less than 3

= -2 Domain: x greater or equal to 3

Find a and b such that f is continuous. - Jul 27th 2006, 11:57 AMearbothQuote:

Originally Posted by**Nimmy**

I've attached a diagram to show you what you have to calculate:

In short: There are 2 points which are connected by a straight line. So you know 2 points of this line. Use the 2-point-formula of a line to get the equation.

(You should get f(x)=-x+1, -1 < x < 3)

Greetings

EB - Jul 27th 2006, 12:22 PMThePerfectHackerQuote:

Originally Posted by**Nimmy**

However we need to check $\displaystyle x=-1,3$

Let us do -1 first,

By definition of countinuity we need that,

$\displaystyle \lim_{x\to -1} f(x)=f(-1)$

Thus,

$\displaystyle \lim_{x\to -1^-}f(x)=\lim_{x\to -1^+}f(x)=2$

But the limit from the left is same as,

$\displaystyle \lim_{x\to -1^-}2=2$

And the limit from the right is same as,

$\displaystyle \lim_{x\to -1^+}ax+b=-a+b$

Thus,

$\displaystyle -a+b=2$

Similarly, if we do this for $\displaystyle x=3$ we have,

$\displaystyle 3a+b=-2$

From these two equations we have,

$\displaystyle a=-1,b=1$