Find the limit $\lim _ { \Delta y \rightarrow 0 } \frac { f ( x , y + \Delta y ) - f ( x , y ) } { \Delta y } \text { for the function } f ( x , y ) = 7 x + 5 x y - 2 y$
A) $5 x - 2$
B) $7 + 5 x$
C) $7 + 5 y$
D) 0
E) $- 2 y$

Question

Find the limit  $\lim _ { \Delta y \rightarrow 0 } \frac { f ( x , y + \Delta y ) - f ( x , y ) } { \Delta y } \text { for the function } f ( x , y ) = 7 x + 5 x y - 2 y$
A) $5 x - 2$
B) $7 + 5 x$
C) $7 + 5 y$
D) 0
E) $- 2 y$

Quizplus · Accepted Answer

This limit represents the partial derivative of the function $f(x, y)$ with respect to $y$, holding $x$ constant. Calculating the partial derivative with respect to $y$ gives $5x - 2$, as the derivative of $7x$ with respect to $y$ is $0$, the derivative of $5xy$ with respect to $y$ is $5x$, and the derivative of $-2y$ with respect to $y$ is $-2$.

Find the Limit A) 5x−25 x - 25x−2 B) 7+5x7 + 5 x7+5x

Find the Limit A) $5 x - 2$ B) $7 + 5 x$