Question

Use the limit definiftion to find m tan of f(x)=1/x at x=3

Answer 1

you f'(x) at x=3 of f(x)=1/x is that correct?

Answer 2

Yes!

Answer 3

I've tried working it out but I keep getting f(3)-f(3)

Answer 4

ok limit definition of derivative
\[f'(a)=\lim_{x\to a} \frac{f(x)-f(a)}{x-a}\]

Answer 5

in your case a=3

Answer 6

so how are you gonna do it?

Answer 7

\[(f(x)-f(3))/x-3\]

Answer 8

yes that good!
so how are you gonna proceed

Answer 9

for x plug in the f(x)=1/x ?

Answer 10

don't forget we are taking the limit

Answer 11

yes f(x)=1/x

Answer 12

f(3)=?

Answer 13

0.33

Answer 14

1/3 is better

Answer 15

leave it as fraction

Answer 16

so we have \[\lim_{x\to 3}\frac{\frac{1}{x}-\frac{1}{3}}{x-3}\]

Answer 17

do we cancel the x?

Answer 18

sorry i was away

Answer 19

how do you cancel x?

Answer 20

We would have to multiply it?

Answer 21

ok try and let me see what you get

Answer 22

\[\frac{ 1-1/3 }{x^2-3 }\]

Answer 23

or would it just be \[\frac{ 1-1/3 }{ 3 }\]

Answer 24

x does not just disappear like that

Answer 25

let's focus on the top alone which is \[\frac{1}{x}-\frac{1}{3}\]
what yo think we can do with this

Answer 26

1/3x?

Answer 27

how?

Answer 28

subtraction of two fractions
you need to find the LCM

Answer 29

How would you do that with an x there?