Math Problem with Limits

[MrCodeDude]

We have students teaching the class this week for extra-credit and this student neglected most of the problems that were on the homework. So I'm clueless

Find the limit (if it exists). (no Graphing Calculator)

lim x->5
5-x
x^2 - 25

I'm lost, x^2 - 25 factors to (x + 5) and (x - 5).

Thanks in advance 🙂

 

[Syringer]

(5-x)/(x+5)(x-5)

Multiply top and bottom by -1

(x-5)/(-x-5)(x-5)

1/(-x-5)

Plug in, 1/(-10)

=-1/10

 

[HappyCracker]

Similarly, you could use L'Hopital's rule, whereby if the limit originally approaches either infinity over infinity or zero over zero, take the derivative of the top and the bottom (separately), then take the limit of that again, you can do this multiple times also.
your case:

lim -x+5
x->5 x^2-25
derivative of top and bottom:
lim -1
x->5 2x
plug in 5, and you get the same answer. just another weapon for your arsenal

 

[Orsorum]

Darnit, they both replied before I got a chance to, but they're both right. I took (5-x) to be the same as (-1)(x-5), which leads to (-1)/(x+5), plug in 5, you get (-1)/(10)

 

[MacBaine]

Originally posted by: HappyCracker
Similarly, you could use L'Hopital's rule, whereby if the limit originally approaches either infinity over infinity or zero over zero, take the derivative of the top and the bottom (separately), then take the limit of that again, you can do this multiple times also.
your case:

lim -x+5
x->5 x^2-25
derivative of top and bottom:
lim -1
x->5 2x
plug in 5, and you get the same answer. just another weapon for your arsenal

You can only use L'hopitals if it is approaching infinity.

The easiest way to do this one is to simply factor out the bottom, which gives you (x+5)(x-5), then cancel the (x-5)s (multiply the top by (-1) and you'll be left with -1/(x+5)

 

[TerryMathews]

Or, if you're halfway intelligent, take the limit as x->4.999 and 5.001, add em together and split the difference.

 

[Gunslinger08]

Originally posted by: TerryMathews
Or, if you're halfway intelligent, take the limit as x->4.999 and 5.001, add em together and split the difference.

Seems halfway stupid to me. Much easier to just factor out (x-5).

Josh