Section 1
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ln(secx+tanx)+C = -ln(secx-tanx)+C
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Mar 1, 2020
Cards (64)
Section 1
(50 cards)
ln(secx+tanx)+C = -ln(secx-tanx)+C
sin(x)+C
sec(x)tan(x)
cf'(x)
Fundamental Theorem of Calculus #2
L'Hopital's Rule
x+c
-cos(x)+C
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).
sec(x)+C
f'(g(x))g'(x)
1
f'(x)-g'(x)
sec²(x)
Horizontal Asymptote
ln(a)*aⁿ+C
Exponential growth (use N= )
-csc²(x)
-cot(x)+C
-ln(cosx)+C = ln(secx)+C
hint: tanu = sinu/cosu
Mean Value Theorem for integrals or the average value of a functions
1
f'(x)+g'(x)
ln(cscx+cotx)+C = -ln(cscx-cotx)+C
Derivative of eⁿ
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.
First Derivative Test for local extrema
Point of inflection at x=k
Global Definition of a Derivative
-sin(x)
f is continuous at x=c if...
uvw'+uv'w+u'vw
nx^(n-1)
cos(x)
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.
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
Fundamental Theorem of Calculus #1
The definite integral of a rate of change is the total change in the original function.
If f and g are inverses of each other, g'(x)
0
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)
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(x)+C
ln(sinx)+C = -ln(cscx)+C
The position function OR s(t)
dy/dx
Derivative of ln(u)
-csc(x)+C
Squeeze Theorem
tan(x)+C
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
Section 2
(14 cards)