Question

Evaluate the following limits: (calculus)

Answer 1

lim: x=5 \[\frac{ |3x+7|-|x+17| }{ x-5}\]

Answer 2

What do you guys think?

Answer 3

do you have the answer? i get 2

Answer 4

Show me how?

Answer 5

I can't figure it out when I have two absolute values

Answer 6

are you familiar with l'Hopital's rule?

Answer 7

lol no

Answer 8

If it's a shortcut to this bs, I am glad to learn it from you. My teacher isn't the best at explaining

Answer 9

well. im sure there's another way that you should be using. you should probably learn that way.


but l'hopital's rule is that:

\[\lim_{x->a}\frac{ f(x) }{ g(x) } = \lim_{x->a}\frac{ f'(x) }{ g'(x) }\]
i split it into two fractions and applied this rule to both

got 3 - 1

Answer 10

if you were to plug in these variables, how would it look like?

Answer 11

@Euler271

Answer 12

\[\lim_{x->5}\frac{ |3x + 7| }{ x - 5 } - \frac{ |x + 17| }{ x-5 } = \lim_{x->5} \frac{ |3| }{1 } -\frac{ |1| }{ 1 }\]

Answer 13

hmm, how did you get one on the bottom and what happened to the +7 and +17

Answer 14

took derivative.

like i said though, there's definitely a different way to do it.

i don't know it though

Answer 15

thanks for the help, i'll use Youtube for further explanation. Thank you so much! @Euler271