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calc 1
differentiation
21
Mathematics
Undergraduate 1
03/07/2011
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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, then
f'(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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