let f(x)= ((3x-1)|x-1|) / (x-1) for x !=0

(a) sketch the graph of f(x)

(b)evaluate lim x->1+ f(x)

(c) evaluate lim x->1- f(x)

(d)evaluate lim x->1 f(x)

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- Oct 9th 2006, 11:51 PMbobby77curve sketching
let f(x)= ((3x-1)|x-1|) / (x-1) for x !=0

(a) sketch the graph of f(x)

(b)evaluate lim x->1+ f(x)

(c) evaluate lim x->1- f(x)

(d)evaluate lim x->1 f(x) - Oct 10th 2006, 05:32 AMCaptainBlack
This behaves linearly in x except when x=1, where there is a jump discontinuity. This is because |x-1|/(x-1) is a constant equal to +1

when x>1, and a constant equal to -1 when x<1.

For x>1 we have:

f(x) = 3x-1

and for x<1, we have:

f(x) = -3x+1,

with a jump discontiuity where f changes grom -2 to the left of x=1

to ~2 to the right of x=1.

Now I have a sketch of this but the upload function appears to be

brocken

Quote:

(b)evaluate lim x->1+ f(x)

1 from above is the limit as x goes to 1 of 3x-1 which is equal to 2.

Quote:

(c) evaluate lim x->1- f(x)

1 from below is the limit as x goes to 1 of -3x+1 which is equal to -2.

Quote:

(d)evaluate lim x->1 f(x)

RonL - Oct 10th 2006, 11:09 AMearboth