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| What is a function of two variables? |
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Definition
a function whose value depends on the changing values of two independently changing variables
in 3-D |
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| What is a function of three variables? |
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Definition
a functions whose value depends on the changing values of three independently changing variables
a 3-D function with respect to time |
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Term
| How do you find the tangent plane to a function of two variable or to a level surface to a function of three variables? |
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Definition
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| Define the linearizaion of f at (a, b)? |
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Definition
| L(a, b) = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b) |
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Term
| State the chain rule for the case where z = f(x, y) and x and y are functions of one variable. |
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Definition
| (dz/dt) = (dz/dx)*(dx/dt) + (dz/dy)*(dy/dt) |
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Term
| If z is defined implicitly as a function of x and y by an equation of the form F(x, y, z) = 0, how do you find dz/dx and dz/dy? |
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Definition
(dz/dx) = (dF/dx)/(dF/dz)
(dz/dy) = (dF/dy)/(dF/dz) |
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Term
| If f is differentiable, write and expression of the directional derivative of f(x0, y0) in the direction of the vector u = <a, b> |
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Definition
Duf(x0, y0) = [image]f(x0, y0) • u
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Term
| Define the gradient vector. |
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Definition
| a vector made up of the partial derivatives of each component of the original vector |
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| State the second derivative test. |
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Definition
D = fxxfyy - (fxy)2
if D < 0 and fxx < 0: local minimum
if D < 0 and fxx > 0: local maximum
if D > 0: saddle point
if D = 0: test fails |
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