Let's denote the three variables as follows:
x = 1.01 , y = 1.05 , z = 1.1
The given expression can be rewritten as:
f(x, y, z) = x y^2 e^z + x \ln(y)
Substitute the given values of x , y , and z into the function f(x, y, z) :
f(1.01, 1.05, 1.1) = 1.01 \times 1.05^2 \times e^{1.1} + 1.01 \times \ln(1.05)
Now, calculate the values:
f(1.01, 1.05, 1.1) = 1.01 \times 1.1025 \times 3.004166 + 1.01 \times \ln(1.05)
f(1.01, 1.05, 1.1) = 1.1426 + 1.01 \times \ln(1.05)
Now, use the third variable function to simplify:
Let's define another function as g(t) = 1.01 \times \ln(t)
So, g(1.05) = 1.01 \times \ln(1.05)
Therefore, the final function becomes:
f(1.01, 1.05, 1.1) = 1.1426 + g(1.05)
Now calculate the value of g(1.05) :
g(1.05) = 1.01 \times \ln(1.05) \approx 1.01 \times 0.04879 \approx 0.0492769
Finally, substitute this value into the original function:
f(1.01, 1.05, 1.1) = 1.1426 + 0.0492769 \approx \boxed{1.19188}