Thread: Dealing with modulus when trying to find limi

Apologies if this is posted in the wrong section.

I am trying to find the limit, as x approaches 3, of


Normally I would multiply/factorise/otherwise rearrange, but unfortunately I seem to have no clue how to add/multiply etc the modulus sections. Any suggestions would be much appreciated

Ivar

Ps: I'm not fussed about the actual answer (my calculator says it's -1/4) but interested in how to deal with the modulus parts

You should be able to finish.

Originally Posted by Ivar_sb

Apologies if this is posted in the wrong section.

I am trying to find the limit, as x approaches 3, of


Normally I would multiply/factorise/otherwise rearrange, but unfortunately I seem to have no clue how to add/multiply etc the modulus sections. Any suggestions would be much appreciated

Ivar

Ps: I'm not fussed about the actual answer (my calculator says it's -1/4) but interested in how to deal with the modulus parts

At x= 3, 5- 2x= 5- 6= -1 so 5- 2x is negative for x close to 3 and |5- 2x|= -(5- 2x)= 2x- 5.

At x= 3, x- 2= 3- 2= 1 so x- 2 is positive for x close to 3 and |x-2|= x-2.

At x= 3, x- 5= 3- 5= -2 so x- 5 is negtive for x close to 3 and |x- 5|= -(x-5)= 5- x.

At x= 3, 3x- 7= 9- 7= 2 so 3x- 7 is positive for x close to 3 and |3x-7|= 3x- 7

That means that


As long as x is not 3, we can cancel those "x-3" terms to get -1/4. The limit of that is, of course, -1/4.

Thanks to both of you, it's actually quite simple once you see the trick. Doh.