Final answer:
To calculate f(8,7), we substitute the values into the function f(x,y) to get -5. For f(8,7.05), we assume the additional 1 in f(8,1,7.05) was a typo, and the result is -5.15. The change in z (Δz) is -0.15.
Step-by-step explanation:
The student is asking for the evaluation of the function f(x,y) = 2x−3y at specific points, and the calculation of Δz. To find f(8,7), we substitute x = 8 and y = 7 into the function:
f(8,7) = 2(8) − 3(7) = 16 − 21 = −5.
However, the request for f(8,1,7.05) appears to be a typo, as the function f(x,y) only takes two arguments. Assuming the intended function is f(8,7.05), we find:
f(8,7.05) = 2(8) − 3(7.05) = 16 − 21.15 = −5.15.
The change in z, or Δz, is the difference in the function's values at the two points:
Δz = f(8,7.05) − f(8,7) = −5.15 − (−5) = −0.15.