Answer
The solutions are
a) $f(5,0) = 5.$
b) $f(3,2) = 3e^2.$
c) $f(2,-1) = \frac{2}{e}.$
d) $f(5,y) = 5e^y.$
e) $f(x,2) = xe^2.$
f) $f(t,t) = te^t.$
Work Step by Step
We will simply substitute $x$ from the first coordinate of a given point and $y$ from the second coordinate from the given point into the $f(x,y)=xe^y$.
a) $f(5,0) = 5\times e^0 = 5.$
b) $f(3,2) = 3\times e^2 = 3e^2.$
c) $f(2,-1) = 2\times e^{-1} = \frac{2}{e}.$
d) $f(5,y) = 5\times e^y = 5e^y.$
e) $f(x,2) = x\times e^2 = xe^2.$
f) $f(t,t) = te^t.$