Limit Problem: 1/b - 1/3 as b approaches 3 | Homework Help

[EvilBunny]

Homework Statement

1/b - 1/3
-----------
b-3



Lim b ----> 3

Homework Equations

The Attempt at a Solution

This is driving me nuts. I always end with 0 but that's not the answer.
I tried direct substitution and it didn't work.

I tried plugging in 2.999999999 but it gives a very small number devided by a very small number

I tried the conjugate and even deviding by the highest power altho that's for infinity.

 

[D H]

You can try this experimentally to see what the limit (if any) appears to be. It takes less than a minute to set this up in an Excel spreadsheet .

You can also try to simplify the expression. What is the numerator?

 

[EvilBunny]

I don't really see how further I can simplyfy

numerator is

1 devided by ''b' minus 1 devided by 3

 

[D H]

Find the common factor.

 

[EvilBunny]

I don't see a common factor in

1/b - 1/3

or

b-3

 

[dynamicsolo]

(1/b) - (1/3)

How do you take the difference of two fractions?

 

[EvilBunny]

woa... nwo seriously how did I miss that. I wasted soo much time on this.

 

[EvilBunny]

well am still stuck.


So I put them on the same denominator and end with


(3-b) / 3 b
-------------
b-3

 

[EvilBunny]

okay -1/9 got it finally . thanks for the help