math_113_20140916033120 Flashcards
The Squeeze Theorem
Don’t know the definition, but you’re supposed to find the range of the function (usually sin or cos, so between -1 and 1) so it is in the format -1
Intermediate Value Theorem
If f(x) is continuous on the closed interval [a,b], let f(a)
Extreme Value Theorem
If f is continuous on a closed and bounded interval [a,b], then f surely attains both an absolute max and an absolute min on [a,b].
Rolle’s Theorem
If f(x) is continuous on [a,b], if f(x) is differentiable on (a,b), and if f(a)=f(b), then there exists a value c in (a,b) such that f’(c)=0.
Mean Value Theorem
If f(x) is continuous on [a,b], and if f(x) is differentiable on (a,b), then there exists a value c in (a,b) where f’(c)=(f(b)-f(a))/(b-a).
Fundamental Theorem of Calculus I
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Fundamental Theorem of Calculus II
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sinx
cosx
cosx
-sinx
tanx
sec^2x
cscx
-cscxcotx
secx
secxtanx
cotx
-csc^2x
Linerization
f(x)=L(x)=f(a)+f’(a)(x-a)
Reimann Sums
A=limit as x approaches infinity of the sum (n on top i=1 on bottom) f(xi)delta(x) where delta(x)=(b-a)/n and xi=a+idelta(x)
First Principles
(f(x+h)-f(x))/h
Steps for Curve Sketching
DISA ILCSDomain, Intercepts, Symmetry, Asymptotes, Intervals of Increase and Decrease, Local Max/Min, Concavity and Inflection Points, Sketch.
Sum (n on top k=1 on bottom) i
(n(n+1))/2
Sum (n on top k=1 on bottom) i^2
(n(n+1)(2n+1))/6
Absolute Maximum or Minimum
If the local max/mins are true for all values of x, then f(c) is an absolute max/min.
Local Minimum
f(x) > or equal to f(c) for all x in some interval.
Local Maximum
f(x)
Critical Number
Place in the domain where f’(x) =0 or where f’(x) DNE.
Increasing Function
If the function is rising to the right.