Section 1
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-csc(x)+C
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Cards (75)
Section 1
(50 cards)
-csc(x)+C
-cot(x)+C
Formula for Washer Method
Axis of rotation is not a boundary of the region.
x+c
Squeeze Theorem
1
cf'(x)
ln(sinx)+C = -ln(cscx)+C
Horizontal Asymptote
tan(x)+C
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.
dy/dx
1
If f and g are inverses of each other, g'(x)
Mean Value Theorem for integrals or the average value of a functions
f'(x)-g'(x)
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.
Global Definition of a Derivative
ln(secx+tanx)+C = -ln(secx-tanx)+C
f'(g(x))g'(x)
First Derivative Test for local extrema
f is continuous at x=c if...
Point of inflection at x=k
-ln(cosx)+C = ln(secx)+C
hint: tanu = sinu/cosu
Formula for Disk Method
Axis of rotation is a boundary of the region.
nx^(n-1)
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).
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
ln(cscx+cotx)+C = -ln(cscx-cotx)+C
sin(x)+C
sec²(x)
L'Hopital's Rule
Exponential growth (use N= )
-csc²(x)
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)
Fundamental Theorem of Calculus #1
The definite integral of a rate of change is the total change in the original function.
-cos(x)+C
0
Fundamental Theorem of Calculus #2
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
sec(x)+C
uvw'+uv'w+u'vw
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.
cos(x)
f'(x)+g'(x)
Area under a curve
ln(x)+C
-sin(x)
The position function OR s(t)
sec(x)tan(x)
Section 2
(25 cards)