Question

Find the Limit

Lim x-5/ (1/x)-(1/5)
x->5

can I assume that 1/x is going to infinity so (1/x) is zero? so then I will be left with:

5-5/ (-1/5)

0/ (-1/5)
=limit is 0?

Answer 1

no, x ---> 5, so 1/x ----> 1/5
you would get 0/0
When that happens, you are guaranteed that your expression factors somehow.

how about multiplying top and bottom by 5x.
Then

lim(5x^2 - 25x)/(5-x) as x ---> 5
= lim 5x(x-5)/(5-x) as x ---> 5
= lim 5x(-1) as x ---> 5
= -25

Answer 2

ahhh i see.
dang, then I got this one wrong on the test.

thank you!