AP Calculus Flash Cards Flashcards
AP Calculus AB, calculus terms and theorems
Terms : Hide Images [1]
| 503752732 | 1 |  | |
| 503752733 | 0 |  | |
| 503752734 | Squeeze Theorem |  | |
| 503752735 | f is continuous at x=c if... |  | |
| 503752736 | 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 | |
| 503752737 | Global Definition of a Derivative |  | |
| 503752738 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  |
| 503752739 | nx^(n-1) |  | |
| 503752740 | 1 |  | |
| 503752741 | cf'(x) |  | |
| 503752742 | f'(x)+g'(x) |  | |
| 503752743 | The position function OR s(t) |  | |
| 503752744 | f'(x)-g'(x) |  | |
| 503752745 | uvw'+uv'w+u'vw |  | |
| 503752746 | cos(x) |  | |
| 503752747 | -sin(x) |  | |
| 503752748 | sec²(x) |  | |
| 503752749 | -csc²(x) |  | |
| 503752750 | sec(x)tan(x) |  | |
| 503752751 | dy/dx |  | |
| 503752752 | f'(g(x))g'(x) |  | |
| 503752753 | 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. | |
| 503752754 | 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) | |
| 503752755 | 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). | |
| 503752756 | 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. |  |
| 503752757 | First Derivative Test for local extrema |  | |
| 503752758 | Point of inflection at x=k |  | |
| 503752759 | 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. |  |
| 503752760 | Horizontal Asymptote |  | |
| 503752761 | L'Hopital's Rule |  | |
| 503752762 | x+c |  | |
| 503752763 | sin(x)+C |  | |
| 503752764 | -cos(x)+C |  | |
| 503752765 | tan(x)+C |  | |
| 503752766 | -cot(x)+C |  | |
| 503752767 | sec(x)+C |  | |
| 503752768 | -csc(x)+C |  | |
| 503752769 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  |
| 503752770 | Fundamental Theorem of Calculus #2 |  | |
| 503752771 | Mean Value Theorem for integrals or the average value of a functions |  | |
| 503752772 | ln(x)+C |  | |
| 503752773 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  |
| 503752774 | ln(sinx)+C = -ln(cscx)+C |  | |
| 503752775 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | |
| 503752776 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | |
| 503752777 | If f and g are inverses of each other, g'(x) |  | |
| 503752778 | Exponential growth (use N= ) |  | |
| 503752779 | Area under a curve |  | |
| 503752780 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  |
| 503752781 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  |
| 503752782 | Inverse Secant Antiderivative |  | |
| 503752783 | Inverse Tangent Antiderivative |  | |
| 503752784 | Inverse Sine Antiderivative |  | |
| 503752785 | Derivative of eⁿ |  | |
| 503752786 | ln(a)*aⁿ+C |  | |
| 503752787 | Derivative of ln(u) |  | |
| 503752788 | Antiderivative of f(x) from [a,b] |  | |
| 503752789 | Opposite Antiderivatives |  | |
| 503752790 | Antiderivative of xⁿ |  | |
| 503752791 | Adding or subtracting antiderivatives |  | |
| 503752792 | Constants in integrals |  | |
| 503752793 | Identity function | D: (-∞,+∞) R: (-∞,+∞) |  |
| 503752794 | Squaring function | D: (-∞,+∞) R: (o,+∞) |  |
| 503752795 | Cubing function | D: (-∞,+∞) R: (-∞,+∞) |  |
| 503752796 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  |
| 503752797 | Square root function | D: (0,+∞) R: (0,+∞) |  |
| 503752798 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  |
| 503752799 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  |
| 503752800 | Sine function | D: (-∞,+∞) R: [-1,1] |  |
| 503752801 | Cosine function | D: (-∞,+∞) R: [-1,1] |  |
| 503752802 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  |
| 503752803 | Greatest integer function | D: (-∞,+∞) R: (-∞,+∞) |  |
| 503752804 | Logistic function | D: (-∞,+∞) R: (0, 1) |  |
| 503752805 | Given f(x): Is f continuous @ C Is f' continuous @ C | Yes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp |  |
| 503752806 | Given f'(x): Is f continuous @ c? Is there an inflection point on f @ C? | This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
Yes f' decreases on X | |