Limits & Instantaneous Rate of Change

[open quail]

Anyone understand Question 6?

[frozen pawn]

Yes we do

Would you be able to do it on another easier function?

Like g(x) = x^2 ?

[open quail]

nah thats just the way the problem is set up i think

[frozen pawn]

Im not asking you to change the problem

I am asking if you would have known

To do it on the function I sent

So that we can at least make sure you know what is being asked of you

(even if u struggle to get to the final form)

[open quail]

ohh

yeah so

[(x+h)^2 - x^2] / h

(x^2 + 2xh +h^2 - x^2)/h

(2xh + h^2) / h

2x + h

h-> 0

2x -> 2(3) = 6

[frozen pawn]

Excellent

So you know exactly where we want to go

Did you write (f(a+h)-f(a))/h

[open quail]

i did

im at [ (sqrt4x+4h-5) - (sqrt4x-5) ] / h rn

[frozen pawn]

The standard trick here

Because you will get stuck

Is to multiply this by

Ok wait

Theres a problem first

Notice the point we are taking

(f(3+h)-f(3))/h

What ure aiming to do is (slightly) harder

Because you didnt choose a particular x

But you do have this luxury

Of taking x = 3

The standard trick is to multiply by $\frac{ \sqrt{4x+4h-5} + \sqrt{4x-5}}{\sqrt{4x+4h-5} + \sqrt{4x-5}}$

[sullen plinth]

Daddy_314

[frozen pawn]

To make a^2-b^2 appear

[open quail]

ohhh i see i see

so it'll be

4x+4h-5 - 4x + 5 numerator

denominator is h [ (sqrt 4x+4h-5) + (sqrt4x-5) ]

then simplify and solve right

[frozen pawn]

Excellent

But x = 3

[open quail]

4 / [ (sqrt 4 x 3 + 4 x 0 - 5) + (sqrt 4 x 3 - 5)

= 4 / sqrt 7 + sqrt 7 = 4/7

[frozen pawn]

You ruined it at the very last step

You dropped the beautiful cake

$\sqrt{7} + \sqrt{7}$ is not 7 !

[sullen plinth]

Daddy_314

[frozen pawn]

You mistook addition for multiplication

[open quail]

whoops...

but yes I understand now tysm for the help

[supple dome]

I thought it was addition too

I get it now though

[frozen pawn]

Welcome