Final - Definations

# Final - Definations - The limit of f(x) as x approaches c...

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FUNCTION: - a function relates each of its inputs to exactly one output. A standard notation for the output of the function f with the input x is f(x). The set of all inputs that a function accepts is called the domain of the function. The set of all outputs is called the range. Derivative:- The limiting value of the ratio of the change in a function to the corresponding change in its independent variable. The instantaneous rate of change of a function with respect to its variable. The slope of the tangent line to the graph of a function at a given point. Also called differential coefficient , fluxion . CONTINUITY:- a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be discontinuous We say that the function f is continuous at some point c when the following two requirements are satisfied: F(c) must be defined (i.e. c must be an element of the domain of f).

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Unformatted text preview: The limit of f(x) as x approaches c must exist and be equal to f(c). (If the point c in the domain of f is not an accumulation point of the domain, then this condition is vacuously true, since x cannot approach c. Thus, for example, every function whose domain is the set of all integers is continuous, merely for lack of opportunity to be otherwise. However, one does not usually talk about continuous functions in this setting.) Relative Maximum:- The highest point in a particular section of a graph. The highest value of y. Relative Minimum:- See above Inflection Points:- An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes Concavity:- Let f ( x ) be a differentiable function on an interval I . Assume that f '( x ) is also differentiable on I . (i) f ( x ) is concave up on I iff on I . (ii) f ( x ) is concave down on I iff on I ....
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## Final - Definations - The limit of f(x) as x approaches c...

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