Question

Evaluate the limit ln lb+2/b+3l as b->infinity

Answer 1

Those are absolute value bars around the numerator and denominator

Answer 2

And I know it goes to 0, but I need to rewrite the numerator and denominator, and my algebra skills are failing me right now T_T

Answer 3

Question for you: as b goes to infinity what is its relationship to 2 or 3?

Answer 4

The 2 and 3 dont matter, so i cancelled them out

Answer 5

good so now what would your fraction be?

Answer 6

think (b+2 + 1)/(b+3) - 1/(b+3)

Answer 7

But then you get an indeterminate form in the ln

Answer 8

because the fraction would become ln linfinity/infinityl

Answer 9

thats not the case. what fraction would you have when you cancel out 2 and 3?

Answer 10

ln lb/bl

Answer 11

ok so if you just saw b/b what woulld you do with that?

Answer 12

Declare it indeterminate and l'Hopital

Answer 13

forget about calculus for a second. pretend you are in algebra class and your teacher said simplify the fraction

Answer 14

You have written "lb+2/b+3l " This is \(\left|b + \dfrac{2}{b} + 3\right|\). The limit does not exist as b increases without bound.

Had you have written "l(b+2)/(b+3)l " This is \(\left|\dfrac{b+2}{b+3}\right|\). The limit does exist as b increases without bound.

You do not need l'Hospiatl. The limit as b increases is 1. Divide Numerator and Denominator by b and show it to be so.

Answer 15

Yes but if you plug in infinity Alex, its indeterminate

Answer 16

Does that not matter?

Answer 17

no no no...you dont plug in infinity until you have reduced it as much as possible

Answer 18

Oh snap, I just realized how stupid I was

Answer 19

b/b=1 T_T

Answer 20

There is no such thing as "plug in". Never do that.
There is no such thing as "cancel". Never do that.
Yes, it is an indeterminate form. Why use an nuclear bomb where a pea shooter will do?

Answer 21

its ok you are learning. these mistakes must be made so they are not repeated in the future.

Answer 22

Because explosions are cool, but I know what you mean

Answer 23

Fair enough. I'll give you that.

Answer 24

Ok so I simplify as far as humanly possible first before I try to evaluate the limit?

Answer 25

yes thats the idea

Answer 26

if you were to plug in points you would see that it is approaching some value.

Answer 27

If you didn't spend enough time with Rational Functions before you got to the Calculus, you will have to go back and get a better background. Rational Functions are important.

Never "plug in". Just resist.

Answer 28

No, I understand. That was just me being a moron. Thanks guys!!!