Question

f(x)=6/(x-6)
The expression inside the limit simplifies to a simple fraction with
numerator =
and denominator =
We can cancel the factor ( ) appearing in the denominator against a similar factor appearing in the numerator leaving a simpler fraction with

numerator =
and denominator =

Answer 1

@ZeHanz

Answer 2

Not much you can do there unless you typed it incorrectly. There are no common factors to cancel.

Answer 3

Really ? :( this is my question

Answer 4

but the first question was saying \[fprime (x)\lim_{t \rightarrow x}\]

Answer 5

@calmat01 is it make sense?

Answer 6

ok, so are you saying you are being asked to take the limit of the function as t approaches x?

Answer 7

Can you give me a picture of the question?

Answer 8

If you can post the question in its entirety, I might be able to figure out what is going on.

Answer 9

ok!

Answer 10

hrer you go,

Answer 11

*here

Answer 12

Great. Now I understand the question. But it looks like part of the problem was cut off. It says your answer above and the next few answers below will involve t and....should that be x?

Answer 13

yes, x. thats right

Answer 14

Okay, so we have to use the definition of the derivative, which in this case is as follows:

\[f \prime(x)=\lim_{t \rightarrow x}\ \frac{ f(x+t)-f(x) }{x- t}\]

Answer 15

yes, i know this part.

Answer 16

i will take note

Answer 17

Ok, so you have used this formula in other problems, correct?

Answer 18

yes, thats correct

Answer 19

ok, so now comes the fun part!

Answer 20

It is going to take me a while to type this up so have a little patience.

Answer 21

I think I am going to use a different program and then upload my answer. Give me a few moments.

Answer 22

ok no problem,

Answer 23

Ok, question for you because I'm dealing with a diffferent issue here. In the fromula I gave you above, is the denominator of the limit t, or x-t in the program you are using because that makes a big difference in the answer.

Answer 24

Nevermind. I just answered my own question.

Answer 25

Here you go, I will be back shortly if you have any questions with it.

Answer 26

thats really cool, thank you .
is this for the first answer?

Answer 27

I got it! but I am not sure where the answers for each questions!

Answer 28

The answer for your first blank is the top line. The derivative definition is modified slightly from what I first put in my initial reply.

Answer 29

The answers to the 2nd and 3rd blanks come from the third line from the bottom of my answer. The numerator is -6(x-t) and the denominator is the product of the three terms (x-t)(x+6)(t+6).

Answer 30

The answer to the fourth blank is the factor that is removed from both the numerator and denominator of my answer.

Answer 31

Tha answer to the fifth and six blanks are fouind in the second step from the bottom of my answer.

Answer 32

The last blank is answered by my last step.