Posted by T.Gracken on October 30, 2002 at 13:22:31:
In Reply to: help with definiations/relations posted by kimCav on October 30, 2002 at 07:41:46:
: I just need a better understanding of the following terms- mostly how they relate to the graph of the function. These are my own words please make corrections or maybe use better wordage.
: dervative- slope of the tangent line of the function
the derivative of a function represents a "rate of change", that is, "how fast is something changing". It can represent the slope of a tangent too!
: antidervative- is the inverse process of a dervative. In words it is the function plus the constant of integration. RIGHT!!!!! The antidervatives are vertical transtions of each other. You can have more than one antidervative when you use + C. (family of the function)
an anti-derivative represents "how much change has occured"
: constant of intergration- is a constant of the general solution the C in G(x)=x^2+C When C has a mulitple values it produces a family of antidervative for the function
this (also) is the term that has no bearing on the derivative of an anti-derivative
: general solution- is the form used when C does not have a value. the C in G(x)=x^2+C Use it when you do not have the initial conditions
yes! when no specifics (or not enough to obtain a finite number of solutions) are provided, it represents all the possibilities given the parameters
: I am still working on trying to understand the following any help would be nice!!!
: indefinite intergral
an indefinite integral is the family of all anti-derivatives for a given function
: definite intergral
a definite integral is (typically defined as) a limit of Riemann sums. It represents the amount of change over an interval
: limits of intergration
the endpoints of the interval being considered for a definite integral
These are just the informal definitions I use. I tend to think of them as in between formal definitions and English definitions. Perhaps others will provide other examples.
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