24 Questions
The rate of change of z with respect to x is represented by ______
Δz/Δx
The total differential of z = f(x, y) is given by ______
dz = ∂f/∂x dx + ∂f/∂y dy
The ______ gives an approximation of the change in the dependent variable given small changes in each of the independent variables.
total differential
The total derivative represents the total change in the dependent variable due to changes in all the ______ variables.
independent
The effect on z of a small change in x is given by the ______ differential.
partial
The total differential is the sum of the ______ differentials.
partial
The total derivative of z with respect to x is ∂z/∂x = ∂f/∂x + ∂f/∂y ⋅ ______ dy/dx
the
∂f/∂x = ______ x^2
6
The total derivative of z with respect to t becomes ∂z/dt = ∂f/∂x ⋅ ______ dt + ∂f/∂y ⋅ dy/dt
dx
The direct effect of x on z, plus the indirect effect of x on z through y is given by the ______ derivative.
total
∂f/∂x = ______ x
-6
The ______ refers to the rate of change of a function.
derivative
A supply function is given by the equation P = ______ Q2
3
Find the derivative of P, the differential of P, and the approximate change in P if Q is increased by ______ %
9
The total differential of z is given by dz = ______dx + ______dy.
∂f/∂x, ∂f/∂y
The ______ of z is given by the partial derivative of z with respect to x and y.
total differential
The formula for the total derivative is given by dz/dx = ______ + ______ * dy/dx.
∂f/∂x, ∂f/∂y
The ______ refers to the actual change in the function that occurs when the independent variable is altered.
differential
The derivative of P is ______________ = 6Q
dP/dQ
The differential of P is dP = ( ______________ )dQ
dP/dQ
The change in Q is ΔQ = ______________ % · Q
9
The approximate change in P is ΔP = ( ______________ )ΔQ
dP/dQ
The annual revenues (R) of Highple Consulting depends on the fees (F), promotions (P), and the number of marketers ( ______________ ).
M
The supply function is given by the equation P = ______________ Q2.
0.5
Learn about incremental changes, partial differentials, and total derivatives. Understand how small changes in independent variables affect dependent variables and calculate rates of change.
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