Question

lim t- squareroot of 3t +4 all over
t->4 4 - t

Answer 1

have you tried multiplying the denominator and numberiation by the conjugate

Answer 2

Yes @lagrangeSon678 is right! multiply top and bottom by
\[t+\sqrt{3t+4}\]

Answer 3

then what?

Answer 4

Then see if the top factors

Answer 5

and then see if something cancels on top and bottom

Answer 6

ontech you got it?

Answer 7

im still @ it.. trying.. not giving up

Answer 8

Let me know if you want me to show you the first step
By the way don't multiply out the bottom

Answer 9

I'm glad you are trying to do it and learn it. That is really cool by the way. You get a medal! :)

Answer 10

ok.. will do.

Answer 11

got -4 for the answer.. not too sure if its correct

Answer 12

Let me check and show
One sec...

Answer 13

\[\lim_{t \rightarrow 4}\frac{t-\sqrt{3t+4}}{4-t} \cdot \frac{t+\sqrt{3t+4}}{t+\sqrt{3t+4}}\]
\[\lim_{t \rightarrow 4}\frac{t^2-(3t+4)}{(4-t)(t+\sqrt{3t+4})}\]
\[\lim_{t \rightarrow 4}\frac{t^2-3t-4}{(4-t)(t+\sqrt{3t+4})}\]
Did you get this far?

Answer 14

\[\lim_{t \rightarrow 4}\frac{(t-4)(t+1)}{-(t-4)(t+\sqrt{3t+4})}\]

Answer 15

Does anything cancel?

Answer 16

yes

Answer 17

the (t-4) will cancel right?

Answer 18

yep

Answer 19

So we have
\[-\lim_{t \rightarrow 4}\frac{t+1}{t+\sqrt{3t+4}}\]

Answer 20

Now you just plug in 4 for t

Answer 21

\[-\frac{4+1}{4+\sqrt{3(4)+4}}\]

Answer 22

ok

Answer 23

do you got it?
any questions with anything I did?

Answer 24

i completely understand what u did.. Thanks so very much.
When doing it on my own, I just dont know when to do what.

Answer 25

Practice practice makes perfect!

Answer 26

Well no one is perfect lol

Answer 27

:)

Answer 28

i have two more with graphs.. do u think u could assist?

Answer 29

Go ahead.

Answer 30

it says sketch graph that illustrates the following : lim f(x) = infinity
x->0+

Answer 31

and lim f(x) = -infinity
x->0-

Answer 32

We get to make up the graph?

Answer 33

so It say we have as x approaches 0 from the right the curve is getting closer to infinity

Answer 34

Now it says as we get close to from the left we have that the curve is getting closer to -infinity
you can use by graph by clicking that pencil to draw this part

Answer 35

so for the second one.. would it look something like this?