Seja f(x,y)=3x+2y. Calcule: f(1,−1); f(a,x); (f(x+h,y)−f(x,y)) / h; (f(x,y+k)−f(x,y)) / k.

Oi, Carolina,

$f(1,-1)=3(1)+2(-1)=3-2=1$f(1,−1)=3(1)+2(−1)=3−2=1

$f(a,x)=3(a)+2(x)=3a+2x$f(a,x)=3(a)+2(x)=3a+2x

$\frac{f(x+h,y)-f(x,y)}{h}=\frac{[3(x+h)+2y]-(3x+2y)}{h}=\frac{3x+3h+2y-3x-2y}{h}=\frac{3h}{h}=3$hf(x+h,y)−f(x,y)​=h[3(x+h)+2y]−(3x+2y)​=h3x+3h+2y−3x−2y​=h3h​=3

$\frac{f(x,y+k)-f(x,y)}{k}=\frac{[3x+2(y+k)]-(3x+2y)}{k}=\frac{3x+2y+2k-3x-2y}{k}=\frac{2k}{k}=2$kf(x,y+k)−f(x,y)​=k[3x+2(y+k)]−(3x+2y)​=k3x+2y+2k−3x−2y​=k2k​=2

Até.