# Shared Flashcard Set

## Details

calc 1
differentiation
21
Mathematics
03/07/2011

Term
 definition of a derivative
Definition
 f'(x)=lim h-0 (f(x+h)-f(x))/h provided that the limit exists.
Term
 the mathmatical definition of continuity
Definition
 a function y=f(x) is continuous at a point c of its domain if: lim x-c f(x)=f(c)
Term
 state the chain rule
Definition
 if f(u) is differentiable at the point u=g(x) and g(x) is differentiable at x, then the composite function f(g(x)) is differentiable at x, and:f(g(x))=f'(g(x))*g'(x)
Term
 extreme value theorum
Definition
 if f is continuous on a closed interval [a,b],then f attains both an absolute max value M and an absolute minimum value m in [a,b]. That is,there are numbers x1 and x2 in [a,b] with f(x1)=m, f(x2)=M, and f(x) is between m and M for every other x in [a,b].
Term
 first derivative theorum
Definition
 if f has a local max or minimum value at an interior point c of its domain, and if f' is defined at c, thenf'(c)=0
Term
 mean value theorum
Definition
 suppose y=f(x) is continuous on a closed interval [a,b],and differentiable on the interval's interior (a,b) at which f(b)-f(a)/b-a = f'(c)
Term
 area of a circle
Definition
 (pi)r^2
Term
 area of a triangle
Definition
 A=1/2 b*h
Term
 area of a parallelogram
Definition
 A=bh
Term
 area of a trapezoid
Definition
 A=1/2(a+b)h
Term
 volume of a sphere
Definition
 4/3(pi)r^3
Term
 surface area of a sphere
Definition
 4(pi)r^2
Term
 volume of a cylinder
Definition
 (pi)r^2 *h
Term
 volume of a cone
Definition
 1/3(pi)r^2 *h
Term
 surface area of a cube
Definition
 6a^2
Term
 f'(x)=sin(x)
Definition
 cos(x)
Term
 f'(x)=cos(x)
Definition
 -sin(x)
Term
 f'(x)=tan(x)
Definition
 sec^2(x)
Term
 f'(x)=sec(x)
Definition
 sec(x)tan(x)
Term
 f'(x)=cot(x)
Definition
 csc^2(x)
Term
 f'(x)=csc(x)
Definition
 -csc(x)cot(x)
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