AP Calculus BC Review Flashcards
Terms : Hide Images [1]
| 6612632254 | Tangent Line | Straight line on the curve at a given point that can be used to estimate values near by | 0 | |
| 6612646273 | Slope | Rise over run |  | 1 |
| 6612654643 | Instantaneous Rate of Change | the rate of change at a particular moment, for F(x) this would be F'(x) | 2 | |
| 6612662488 | Average Rate of Change | the change in the value of a quantity divided by the elapsed time |  | 3 |
| 6612677976 | Average Value | finds the average value of a function. often related to the mean value theorem |  | 4 |
| 6612698439 | Linear Approximation | Using the tangent line to approximate nearby values |  | 5 |
| 6612717690 | Displacement | The distance and direction of an object's change in position from the starting point. function is given in relation to time | 6 | |
| 6612709251 | Velocity | The speed at which an object is traveling velocity function is the derivative of a position function in relation to time. | 7 | |
| 6612713460 | Acceleration | The rate at which velocity changes Acceleration function is the derivative of a velocity function in relation to time | 8 | |
| 6612722472 | Total Distance | Total distance traveled to do this calculate integral of velocity graph positive and negative sections separately and add absolute value of those together. | 9 | |
| 6612737668 | Speeding Up | Acceleration has the same sign as Velocity | 10 | |
| 6612739240 | Slowing Down | Acceleration has the opposite sign as Velocity | 11 | |
| 6612741475 | Area Under the Curve | Integral or antiderivative | 12 | |
| 6612751729 | Area Between Curves | with f(x) on top and g(x) on bottom a and b represent bounds or where the two graphs intersect |  | 13 |
| 6612761492 | Disc Method of Rotation | V = pi * int from a to b of R(x)^2 dx R(x) is radius and dx is height rotated around variable inside | 14 | |
| 6612796295 | Washer Method of Rotation | V = pi * int from a to b of ( R(x)^2 - r(x) ^2 ) dx R(x) is furthest away from axis r(x) is closest to axis rotated around variable inside | 15 | |
| 6612808480 | Shell Method of Rotation | V = 2pi * int from a to b of ( x * F(x) ) dx rotated around opposite variable inside | 16 | |
| 6612819239 | Definition of A Derivative | we say that f is differentiable at x = a and the limit is the derivative of f(x) at x = a, denoted by f prime of a. |  | 17 |
| 6612827281 | Continuity | A function is uninterrupted, this implies integratibility | 18 | |
| 6612843634 | Product Rule |  | 19 | |
| 6612845422 | Quotient Rule |  | 20 | |
| 6612847209 | Chain Rule | also applies to Trig functions, natural logs, and e |  | 21 |
| 6612851540 | U-Substitution |  | 22 | |
| 6612854570 | Integration by Parts | int u dv = u v - int v du | 23 | |
| 6612866715 | Partial Fractions | Splitting up a fraction into its parts can make integration easier! |  | 24 |
| 6612875446 | Slope Fields | Drawing the slopes at different points for a function (often that is difficult to integrate) can help predict the shape of the function |  | 25 |
| 6612882036 | Particular Solution | Integration that has value for c solved for by plugging in a known coordinate pair | 26 | |
| 6612885713 | Euler's Method | a method of approximation helpful when dy/dx has x and y terms in it |  | 27 |
| 6612896119 | g(x) is increasing | g'(x) is positive | 28 | |
| 6612897347 | g(x) is decreasing | g'(x) is negative | 29 | |
| 6612898046 | g(x) is concave up | g''(x) is positive | 30 | |
| 6612899721 | g(x) is concave down | g''(x) is negative | 31 | |
| 6612901931 | g(x) changes directions | g'(x) passes through 0 | 32 | |
| 6612903767 | g(x) has a point of inflection | g''(x) passes through 0 or DNE | 33 | |
| 6612950604 | Local/Relative Maximum | A point on the graph of a function where no other nearby points have a greater y-coordinate. | 34 | |
| 6612952292 | Local/Relative Minimum | A point on the graph of a function where no other nearby points have a lesser y-coordinate. | 35 | |
| 6612954809 | Absolute Maximum | The y-value of a point on a graph that is higher than any of the other points on the entire graph. Needs to be proved with critical points and the limits as x approaches - infinity and + infinity | 36 | |
| 6612959043 | Absolute Minimum | The lowest point of the function Needs to be proved with critical points and the limits as x approaches - infinity and + infinity | 37 | |
| 6612967578 | Stationary Points | Maximum Points, Minimum Points, and Points of Inflection | 38 | |
| 6612968672 | Critical Point | Occurs when f'(x) = 0 Can be a min, max, or neither | 39 | |
| 6613126168 | Related Rates | A class of problems in which rates of change are related by means of differentiation. Standard examples include water dripping from a cone-shaped tank and a man's shadow lengthening as he walks away from a street lamp. | 40 | |
| 6613128994 | Riemann Sums | A Riemann Sum is a method for approximating integrals |  | 41 |
| 6613147220 | Trapezoidal Sums | Riemann Sums done with averaging two points instead of picking a side can be more accurate | 42 | |
| 6613155966 | Mean Value Theorem | the average value on a certain integral must have a value of x that it is equal to |  | 43 |
| 6613168094 | Intermediate Value Theorem |  | 44 | |
| 6613175392 | Extreme Value Theorem |  | 45 | |
| 6613180228 | 1st Fundamental Theorem of Calc | int from a to b of f'(x) dx = f(b) - f(a) | 46 | |
| 6613221003 | 2nd Fundamental Theorem of Calc | d/dx (int from c to x of f(t) dt) = f(x) | 47 | |
| 6613231606 | L'Hopital's Rule | if lim x --> of g(x)/f(x) is 0/0 then you can derive |  | 48 |
| 6613237787 | Find int 0 to infinity of f(x) dx | substitute b and do lim as b--> infinity | 49 | |
| 6613259029 | Polar Coordinates | (r,theta) |  | 50 |
| 6613263399 | Polar Derivatives | dy/dx = (dy/dtheta)/(dx/dtheta) | 51 | |
| 6613279252 | Polar Length of Curve | int of alpha to beta of sqrt ( (dx/dtheta)^2 + (dy/dtheta)^2) | 52 | |
| 6613283358 | Polar Integrals | 0.5 int from alpha to beta r^2 dtheta = area | 53 | |
| 6613288514 | Parametric Coordinates | (x(t),y(t)) | 54 | |
| 6613288515 | Parametric Derivatives | dy/dx = (dy/dt)/(dx/dt) d2y/dx2 = (d/dt(dy/dt))/(dx/dt) | 55 | |
| 6613289762 | Parametric Length of Curve | int of a to b of sqrt ( (dx/dt)^2 + (dy/dt)^2) | 56 | |
| 6613293184 | Parametric Integrals | integrals normal but with position vectors and relative to t | 57 | |
| 6613320280 | Particle motion | s = ( x(t) , y(t) ) v = ( x'(t), y'(t) ) a = ( x''(t), y''(t) ) | 58 | |
| 6613325555 | Magnitude | || v(t) || = sqrt ( ((dx/dt)^2) + ((dy/dt)^2) ) | 59 | |
| 6613331330 | Series for sin x |  | 60 | |
| 6613351564 | Series for cos x |  | 61 | |
| 6613352795 | series for e^x | e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... | 62 | |
| 6613360403 | Maclaurin Series | a Taylor series about x=0 |  | 63 |
| 6613366426 | Taylor Series | if the function f is smooth at x=a, then it can be approximated by the nth degree polynomial f(x) ~ f(a) + f'(a)(x-a) + f"(a)(x-a)^2/2! + ... + f^n(a)(x-a)^n/n! |  | 64 |
| 6613375020 | nth term test for divergence |  | 65 | |
| 6613376531 | p-series test |  | 66 | |
| 6613383728 | Geometric Series Test | An = a r^(n-1) , n>= 1 |r| < 1 converges to a/(1-r) | 67 | |
| 6613400420 | Alternating Series Test | An = (-1)^n bn , bn>=0 is bn+1 <= bn and lim n-> infinity of bn=0 series converges |  | 68 |
| 6613408856 | Direct Comparison Test |  | 69 | |
| 6613415045 | Limit Comparison Test |  | 70 | |
| 6613418894 | Ratio Test | lim n-> inf |(An+1 / An)| < 1 series converges | 71 | |
| 6613425611 | Interval of Convergence | Determined using ratio of convergence |  | 72 |
| 6613439454 | Power Series | sum from n to infinity of (a*x^x) | 73 | |
| 6613454279 | Lagrange Error Bound |  | 74 |