AP Cal Flashcards
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| 14675236117 | Squeeze Theorem | If f(x) ≤ g(x) ≤ h(x) for all x ̸= a and limx→a f(x) = limx→a h(x) = L, then limx→a g(x) = L | 0 | |
| 14675236118 | Intermediate Value Theorem (IVT) | If f is continuous on [a,b] and k is any number between f(a) and f(b), then there exists at least one number c such that f(c)=k | 1 | |
| 14675236180 | Global Definition of a Derivative |  | 2 | |
| 14675236119 | cosx | -sinx | 3 | |
| 14675236120 | sinx | cosx | 4 | |
| 14675236121 | sec²x | tanx | 5 | |
| 14675236122 | -csc²x | cotx | 6 | |
| 14675236123 | secxtanx | secx | 7 | |
| 14675236124 | 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. | 8 | |
| 14675236125 | Mean Value Theorem | if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b) | 9 | |
| 14675236126 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 10 |
| 14675236127 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 11 |
| 14675236128 | 2nd derivative is zero | point of inflection | 12 | |
| 14675236129 | f '' is negative | concave down, relative max | 13 | |
| 14675236130 | f ' is positive | concave up, relative minimum | 14 | |
| 14675236131 | d/dx (x^n) | nx^n-1 | 15 | |
| 14675236132 | d/dx (fg) | fg' + gf' | 16 | |
| 14675236133 | d/dx (f/g) | (gf'-fg')/g^2 | 17 | |
| 14675236134 | d/dx (f(g(x))) | f'(g(x))g'(x) | 18 | |
| 14675236135 | d/dx (e^x) | e^x | 19 | |
| 14675236136 | d/dx (a^x) | a^x ln(a) | 20 | |
| 14675236137 | d/dx (ln x) | 1/x | 21 | |
| 14675236138 | Indefinite integral of dx | x+c | 22 | |
| 14675236139 | indefinite integral (1/x) dx | ln |x| + C | 23 | |
| 14675236140 | indefinite integral (e^x) dx | e^x + C | 24 | |
| 14675236141 | indefinite integral (a^x) dx | a^x/ln(a) + C | 25 | |
| 14675236142 | indefinite integral (x^n) dx | (x^(n+1))/(n+1) + C (if n not = -1) | 26 | |
| 14675236143 | indefinite integral (sin x) dx | -cos x + C | 27 | |
| 14675236144 | indefinite integral (cos x) dx | sin x + C | 28 | |
| 14675236145 | indefinite integral (tan x) dx | ln |sec x| + C OR -ln |cos x| + C | 29 | |
| 14675236146 | indefinite integral (cot x) dx | ln |sin x| + C | 30 | |
| 14675236147 | indefinite integral (sec x) dx | ln |sec x + tan x| + C | 31 | |
| 14675236148 | indefinite integral (csc x) dx | ln |csc x - cot x| + C | 32 | |
| 14675236149 | indefinite integral (sec^2 x) dx | tan x + C | 33 | |
| 14675236150 | indefinite integral (sec x tan x) dx | sec x + C | 34 | |
| 14675236151 | indefinite integral (csc^2 x) dx | -cot x + C | 35 | |
| 14675236152 | indefinite integral (csc x cot x) dx | -csc x + C | 36 | |
| 14675236153 | indefinite integral (tan^2 x) dx | tan x - x + C | 37 | |
| 14675236154 | indefinite integral (1/(a^2 + x^2)) dx | (1/a)(tan^-1 (x/a)) + C | 38 | |
| 14675236155 | ndefinite integral (1/(sqrt(a^2 - x^2))) dx | sin^-1 (x/a) + C | 39 | |
| 14675236156 | absolute maximum | the highest point on a graph | 40 | |
| 14675236157 | absolute minimum | the lowest point on a graph | 41 | |
| 14675236158 | local maximum | Biggest y-value in a small area | 42 | |
| 14675236159 | Local Minimum | Smallest y-value in a small area | 43 | |
| 14675236160 | critical point | A point in which the derivative is zero or undefined | 44 | |
| 14675236161 | concavity | State of curving inward | 45 | |
| 14675236162 | Inflection Points | The points at which the curve changes from curving upward to curving downward | 46 | |
| 14675236163 | End Behavior | The behavior of the graph as x approaches positive infinity or negative infinity. | 47 | |
| 14675236164 | Asymptote | a line that a graph approaches but never crosses | 48 | |
| 14675236165 | root | a solution of an equation | 49 | |
| 14675236166 | cusp | a pointed end where two curves meet | 50 | |
| 14675236167 | Point where a graph changes concavity | point of inflection | 51 | |
| 14675236168 | Area of Triangle | A=1/2bh | 52 | |
| 14675236169 | Area of Circle | A=πr² | 53 | |
| 14675236170 | Circumference of a circle | 2πr | 54 | |
| 14675236171 | Point slope equation of a line | y-y = m(x-x) | 55 | |
| 14675236172 | Slope-intercept equation of a line | y=mx+b | 56 | |
| 14675236181 | Quadratic Formula |  | 57 | |
| 14675236173 | Velocity (in terms of position) | ds/dt ; derivative of position | 58 | |
| 14675236174 | Acceleration (in terms of velocity) | dv/dt ; derivative of velocity | 59 | |
| 14675236175 | Acceleration (in terms of position) | d^2s/dt^2 ; 2nd derivative of position | 60 | |
| 14675236176 | increasing speed | Velocity and acceleration have same sign | 61 | |
| 14675236177 | decreasing speed | Velocity and acceleration have different signs | 62 | |
| 14675236178 | left riemann sum | use rectangles with left-endpoints to evaluate integral (estimate area) | 63 | |
| 14675236179 | right riemann sum | use rectangles with right-endpoints to evaluate integrals (estimate area) | 64 |