Section 1
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Horizontal Asymptote
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Last updated
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Date created
Mar 1, 2020
Cards (64)
Section 1
(50 cards)
Horizontal Asymptote
Mean Value Theorem
The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
Critical Number
If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)
f'(x)-g'(x)
0
sec²(x)
ln(cscx+cotx)+C = -ln(cscx-cotx)+C
Mean Value Theorem for integrals or the average value of a functions
Derivative of eⁿ
Global Definition of a Derivative
ln(sinx)+C = -ln(cscx)+C
x+c
1
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k
cos(x)
tan(x)+C
-csc²(x)
f is continuous at x=c if...
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
Fundamental Theorem of Calculus #1
The definite integral of a rate of change is the total change in the original function.
sec(x)tan(x)
If f and g are inverses of each other, g'(x)
The position function OR s(t)
f'(g(x))g'(x)
dy/dx
Rolle's Theorem
Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).
-cos(x)+C
1
f'(x)+g'(x)
First Derivative Test for local extrema
-cot(x)+C
L'Hopital's Rule
Exponential growth (use N= )
Combo Test for local extrema
If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c. If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c.
ln(a)*aⁿ+C
uvw'+uv'w+u'vw
ln(secx+tanx)+C = -ln(secx-tanx)+C
Derivative of ln(u)
cf'(x)
sin(x)+C
Extreme Value Theorem
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.
-sin(x)
Squeeze Theorem
nx^(n-1)
-csc(x)+C
sec(x)+C
Fundamental Theorem of Calculus #2
ln(x)+C
-ln(cosx)+C = ln(secx)+C
hint: tanu = sinu/cosu
Point of inflection at x=k
Section 2
(14 cards)