limits question: f(x)=9x^2−4x+9.
Then:
lim
h⟶0 f(x+h)−f(x) / h =____

I'm guessing I have to factor out the first function and once I get a value for x, I sub it in for the lim. I'm having difficulties factoring it out though.

Question

limits question: f(x)=9x^2−4x+9.
Then:
lim
h⟶0     f(x+h)−f(x) / h =____

I'm guessing I have to factor out the first function and once I get a value for x, I sub it in for the lim. I'm having difficulties factoring it out though.

hartnn · Answer

what u got as f(x+h) ?

anonymous · Answer

what do you mean?

anonymous · Answer

I thought i'd have to factor out the function first...the quadratic function and solve for x?

hartnn · Answer

to find f(x+h)
we need to plug in 'x+h' instead of every x, in f(x)

anonymous · Answer

i've been stuck on this for the last hour...

anonymous · Answer

I thought i'd have to factor out the function first...the quadratic function and solve for x?

hartnn · Answer

not required , 
first find f(x+h)

anonymous · Answer

$$9x^2+9h^2+18xh-4x-4h+9$$

anonymous · Answer

is that what you mean? sorry I got disconnected from this site.

hartnn · Answer

correct!
now the numerator is f(x+h)-f(x)
find this,
and see what cancels out

anonymous · Answer

but after i do that i get: 9h+18x-4

hartnn · Answer

absolutely correct!
the 'h's got cancelled, right ? :) 

now you can just plug in h=0 in that expression :)

anonymous · Answer

yes! thank-you, genius!

hartnn · Answer

welcome ^_^

anonymous · Answer

oh no, i ended up with 9h+18x-4 and solved for x = 2/9, but when i went to go submit that it turned out incorrect

hartnn · Answer

when u put h=0
you just get 18x-4
thats your answer
no need to solve

anonymous · Answer

ahhhh, that came out as correct! why don't we need to solve it though?

hartnn · Answer

nopes. 
you already solved that limit by plugging h=0

anonymous · Answer

oh i see, thanks a lot! xo.

hartnn · Answer

welcome ^_^