A. 5x and 2y
B. 3 and x
C. 5x and x
D. 4
Answer:
The magnitude is ![\Delta f(0,8) = 72](https://tex.z-dn.net/?f=%5CDelta%20f%280%2C8%29%20%20%3D%20%2072)
The direction is
i.e toward the x-axis
Step-by-step explanation:
From the question we are told that
The function is ![f(x, y) = 9sin(xy) \ \ \](https://tex.z-dn.net/?f=f%28x%2C%20y%29%20%3D%20%209sin%28xy%29%20%5C%20%5C%20%5C)
The point considered is ![(0,8 )](https://tex.z-dn.net/?f=%280%2C8%20%29)
Generally the maximum rate of change of f at the given point and the direction is mathematically represented as
![\Delta f(x,y) = [\frac{\delta (9sin(xy))}{\delta x} i + \frac{\delta (9sin(xy))}{\delta y} i ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20x%7D%20i%20%20%2B%20%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20y%7D%20i%20%20%20%5D)
![\Delta f(x,y) = [9y cos (x,y) i + 9xcos (x,y) j]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%5B9y%20cos%20%28x%2Cy%29%20i%20%2B%20%209xcos%20%28x%2Cy%29%20j%5D)
At ![(0,8 )](https://tex.z-dn.net/?f=%280%2C8%20%29)
![\Delta f (0,8) = [9(8) cos(0* 8)i + 9(8) sin(0* 8)j ]](https://tex.z-dn.net/?f=%5CDelta%20%20f%20%280%2C8%29%20%3D%20%20%5B9%288%29%20cos%280%2A%208%29i%20%20%2B%209%288%29%20sin%280%2A%208%29j%20%20%5D)
![\Delta f (0,8) = 72 i](https://tex.z-dn.net/?f=%5CDelta%20%20f%20%280%2C8%29%20%3D%2072%20i%20)
1st part is c
2nd part is d
I BELIEVE
Answer:
bye
Step-by-step explanation:
bye
1/3 with a line over the answer ( 0.66666666666...)