Limits

[TSN79]

I have a function z=2x^3+xy^2-6y
I need to find the limit of the following:
\lim_{\substack{h\rightarrow 0}} \frac{f(1+h,2)-f(1,2)}{h}
I don't know if the function is required to calculate this limit, so I just wrote it as well. I just need some hint on where to begin, and how to approach this type of limit...

[Tide]

Replace x and y with the specified values, expand your polynomials, subtract, look for cancellation and divide the result by h - then take your limit! :-)

[TSN79]

Won't I need to find the partial derivatives?

[Tide]

That's exactly what you're doing.

[TSN79]

Hmm...I should replace x and y with the specified values, those are 1 and 2 ?
If I do that in the function then I get the value -6. Where does that leave me?

[Tide]

No, (x, y) = (1, 2) for f(1, h) but (x, y) = (1+h, 2) for f(1+h, 2).