Multivariable calculus

[missbrunkow]

Its been forever since i took algebra and cannot remember where to begin with this problem. HELP PLEASE!
For the function f(x,y)=X^2=2y^2 find f(x+h,y)-f(x,y)/k

THanks.

 

[srmichael]

Its been forever since i took algebra and cannot remember where to begin with this problem. HELP PLEASE!
For the function f(x,y)=X^2=2y^2 find f(x+h,y)-f(x,y)/k

THanks.

Is that second equal sign supposed to be there?? Is it either:

\(\displaystyle \displaystyle f(x,y)=x^2+2y^2 or f(x,y)=x^2-2y^2\)

What have you tried so far?

 

[missbrunkow]

i'm very sorry it is: For the function f(x,y)=X^2+2y^2 find f(x+h,y)-f(x,y)/k
i know that
X²+2y² is plugged in for f(x,y) but im not sure what to do with the beginning part with the +h?

 

[pka]

\(\displaystyle \dfrac{f(x+h,y)}{k}=\dfrac{(x+h)^2+2y^2}{k}\)

 

[srmichael]

i'm very sorry it is: For the function f(x,y)=X^2+2y^2 find f(x+h,y)-f(x,y)/k
i know that
X²+2y² is plugged in for f(x,y) but im not sure what to do with the beginning part with the +h?

Treat x+h as if it were a number and substitute "x+h" in for "x" in the equation. So you then have:

\(\displaystyle \displaystyle f(x+h,y)=(x+h)^2+2y^2=x^2+2xh+h^2+2y^2\) after expanding \(\displaystyle \displaystyle (x+h)^2\)

From there you can then subract f(x,y) and then divide which leads me to this question....Are you sure that it is not supposed to be an "h" in the denominator and not a "k"? They are typically the same in these kinds of problems as you end up cancelling out the denominator from the numerator, yet that is impossible if it is an "h" in the numerator and a "k" in the denominator.

I assume, also, that the you are dividing f(x+h,y)-f(x,y) all by k (or h) and not just f(x,y). It's hard to tell the way you wrote it.