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Calculus

# Calculus - Review of Calculus Derivatives Definition of...

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1 Review of Calculus Derivatives: Definition of Derivative In geometric terms, the derivative is the slope of a curve at a particular point. using an alternative definition, if x + h = c, then Definition of a partial derivative This occurs when we hold all but one of the independent variables of a function constant and is written by or f x (x,y,z). Here x is allowed to change and y and z are considered constant. Differentiable A function, f(x,y) is differentiable at (x o ,y o ) if f x (x o ,y o ) and f y (x o ,y o ) exist plus other conditions that are related to being continuous. We call f differentiable if it is differentiable at every point in its domain. Note: 1) if the partial derivatives f x and f y of a function f(x,y) are continuous throughout an open region R, then f is differentiable at every point in R. 2) If a function f(x,y) is differentiable at (x o ,y o ) then f is continuous at (x o ,y o ) Integrals: Definition of an integral: In geometric terms, the integral is the area under a curve.

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Calculus - Review of Calculus Derivatives Definition of...

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