Question

help limits;

Answer 1

If x is just greater than 3, is the value of the expression pos or neg?

Answer 2

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~3^+}\frac{x+4}{x-3}}\)

when you say, \(\large\color{slate}{\displaystyle x \rightarrow ~3^+}\), you are telling me that you are going to be choosing x-values that are a little greater than 3, but the closer 'x' gets to 3, the smaller the difference between it and the 3 is going to be.

So, as \(\large\color{slate}{\displaystyle x \rightarrow ~3^+}\) then \(\large\color{slate}{\displaystyle (x-3) \rightarrow ~0}\), but it will not be zero, rather it will be an infinitely small decimal in the denominator.

Answer 3

And infinitely small decimal in the denominator, and in the numerator you will have approximately 7.

Answer 4

And remember, that the closer x approaches 3 from the right, the smaller [positive] decimal 'x-3' is going to give you....

Answer 5

So `(approximately 7 / an infinitely small decimal)` is equivalent to what ?

Answer 6

Like we already know it goes to one of the infinities
so we just need to determine if is positive or negative
I'm going to give you an example:
Suppose we looked to the left (instead of right)
x->3^- means x<3
subtracting 3 on both sides gives x-3<0
the factor x-3 is therefore negative for x values to the left of 3
and as @SolomonZelman said x+4 is positive for x values very close to 3 from either direction

so you have +/- in the case where x<3 and and really close to x=3
and you know +/-=-

--

Answer 7

@freckles is it negative then?

Answer 8

for x->3^-

Answer 9

I didn't want to do your problem so I said suppose we look from the left instead of right

Answer 10

idk?

Answer 11

well if x->3^+ doesn't that mean x>3 ?

Answer 12

i guess?

Answer 13

you know that is true
any value to to the right of 3 is greater than 3
x->3^+ this means values of x to the right of 3 as x approaches 3

Answer 14

if x->3^+ then x>3
subtracting 3 on both sides means x-3>0
what does x-3>0 mean about the factor (x-3) in
\[\lim_{x \rightarrow 3^+}\frac{x+4}{x-3}\]

Answer 15

oh.