Statesville Christian School AP Calculus Class
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| 735253488 | Intermediate Value Theorem | If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. | 0 | |
| 735253489 | Average Rate of Change | Slope of secant line between two points, use to estimate instantanous rate of change at a point. | 1 | |
| 735253490 | Instantenous Rate of Change | Slope of tangent line at a point, value of derivative at a point | 2 | |
| 735253491 | Formal definition of derivative | limit as h approaches 0 of [f(a+h)-f(a)]/h | 3 | |
| 735253492 | Alternate definition of derivative | limit as x approaches a of [f(x)-f(a)]/(x-a) | 4 | |
| 735253493 | When f '(x) is positive, f(x) is | increasing | 5 | |
| 735253494 | When f '(x) is negative, f(x) is | decreasing | 6 | |
| 735253495 | When f '(x) changes from negative to positive, f(x) has a | relative minimum | 7 | |
| 735253496 | When f '(x) changes fro positive to negative, f(x) has a | relative maximum | 8 | |
| 735253497 | When f '(x) is increasing, f(x) is | concave up | 9 | |
| 735253498 | When f '(x) is decreasing, f(x) is | concave down | 10 | |
| 735253499 | When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a | point of inflection | 11 | |
| 735253500 | When is a function not differentiable | corner, cusp, vertical tangent, discontinuity | 12 | |
| 735253501 | Product Rule | uv' + vu' | 13 | |
| 735253502 | Quotient Rule | (uv'-vu')/v² | 14 | |
| 735253503 | Chain Rule | f '(g(x)) g'(x) | 15 | |
| 735253504 | y = x cos(x), state rule used to find derivative | product rule | 16 | |
| 735253505 | y = ln(x)/x², state rule used to find derivative | quotient rule | 17 | |
| 735253506 | y = cos²(3x) | chain rule | 18 | |
| 735253507 | Particle is moving to the right/up | velocity is positive | 19 | |
| 735253508 | Particle is moving to the left/down | velocity is negative | 20 | |
| 735253509 | absolute value of velocity | speed | 21 | |
| 735253510 | y = sin(x), y' = | y' = cos(x) | 22 | |
| 735253511 | y = cos(x), y' = | y' = -sin(x) | 23 | |
| 735253512 | y = tan(x), y' = | y' = sec²(x) | 24 | |
| 735253513 | y = csc(x), y' = | y' = -csc(x)cot(x) | 25 | |
| 735253514 | y = sec(x), y' = | y' = sec(x)tan(x) | 26 | |
| 735253515 | y = cot(x), y' = | y' = -csc²(x) | 27 | |
| 735253516 | y = sin⁻¹(x), y' = | y' = 1/√(1 - x²) | 28 | |
| 735253517 | y = cos⁻¹(x), y' = | y' = -1/√(1 - x²) | 29 | |
| 735253518 | y = tan⁻¹(x), y' = | y' = 1/(1 + x²) | 30 | |
| 735253519 | y = cot⁻¹(x), y' = | y' = -1/(1 + x²) | 31 | |
| 735253520 | y = e^x, y' = | y' = e^x | 32 | |
| 735253521 | y = a^x, y' = | y' = a^x ln(a) | 33 | |
| 735253522 | y = ln(x), y' = | y' = 1/x | 34 | |
| 735253523 | y = log (base a) x, y' = | y' = 1/(x lna) | 35 | |
| 735253524 | To find absolute maximum on closed interval [a, b], you must consider... | critical points and endpoints | 36 | |
| 735253525 | 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) f '(c) = [f(b) - f(a)]/(b - a) | 37 | |
| 735253526 | If f '(x) = 0 and f"(x) > 0, | f(x) has a relative minimum | 38 | |
| 735253527 | If f '(x) = 0 and f"(x) < 0, | f(x) has a relative maximum | 39 | |
| 735253528 | Linearization | use tangent line to approximate values of the function | 40 | |
| 735253529 | rate | derivative | 41 | |
| 735253530 | left riemann sum | use rectangles with left-endpoints to evaluate integral (estimate area) | 42 | |
| 735253531 | right riemann sum | use rectangles with right-endpoints to evaluate integrals (estimate area) | 43 | |
| 735253532 | trapezoidal rule | use trapezoids to evaluate integrals (estimate area) | 44 | |
| 735253533 | [(h1 - h2)/2]*base | area of trapezoid | 45 | |
| 735253534 | definite integral | has limits a & b, find antiderivative, F(b) - F(a) | 46 | |
| 735253535 | indefinite integral | no limits, find antiderivative + C, use inital value to find C | 47 | |
| 735253536 | area under a curve | ∫ f(x) dx integrate over interval a to b | 48 | |
| 735253537 | area above x-axis is | positive | 49 | |
| 735253538 | area below x-axis is | negative | 50 | |
| 735253539 | average value of f(x) | = 1/(b-a) ∫ f(x) dx on interval a to b | 51 | |
| 735253540 | If g(x) = ∫ f(t) dt on interval 2 to x, then g'(x) = | g'(x) = f(x) | 52 | |
| 735253541 | Fundamental Theorem of Calculus | ∫ f(x) dx on interval a to b = F(b) - F(a) | 53 | |
| 735253542 | To find particular solution to differential equation, dy/dx = x/y | separate variables, integrate + C, use initial condition to find C, solve for y | 54 | |
| 735253543 | To draw a slope field, | plug (x,y) coordinates into differential equation, draw short segments representing slope at each point | 55 | |
| 735253544 | slope of horizontal line | zero | 56 | |
| 735253545 | slope of vertical line | undefined | 57 | |
| 735253546 | methods of integration | substitution, parts, partial fractions | 58 | |
| 735253547 | use substitution to integrate when | a function and it's derivative are in the integrand | 59 | |
| 735253548 | use integration by parts when | two different types of functions are multiplied | 60 | |
| 735253549 | ∫ u dv = | uv - ∫ v du | 61 | |
| 735253550 | use partial fractions to integrate when | integrand is a rational function with a factorable denominator | 62 | |
| 735253551 | dP/dt = kP(M - P) | logistic differential equation, M = carrying capacity | 63 | |
| 735253552 | P = M / (1 + Ae^(-Mkt)) | logistic growth equation | 64 | |
| 735253553 | given rate equation, R(t) and inital condition when t = a, R(t) = y₁ find final value when t = b | y₁ + Δy = y Δy = ∫ R(t) over interval a to b | 65 | |
| 735253554 | given v(t) and initial position t = a, find final position when t = b | s₁+ Δs = s Δs = ∫ v(t) over interval a to b | 66 | |
| 735253555 | given v(t) find displacement | ∫ v(t) over interval a to b | 67 | |
| 735253556 | given v(t) find total distance travelled | ∫ abs[v(t)] over interval a to b | 68 | |
| 735253557 | area between two curves | ∫ f(x) - g(x) over interval a to b, where f(x) is top function and g(x) is bottom function | 69 | |
| 735253558 | volume of solid with base in the plane and given cross-section | ∫ A(x) dx over interval a to b, where A(x) is the area of the given cross-section in terms of x | 70 | |
| 735253559 | volume of solid of revolution - no washer | π ∫ r² dx over interval a to b, where r = distance from curve to axis of revolution | 71 | |
| 735253560 | volume of solid of revolution - washer | π ∫ R² - r² dx over interval a to b, where R = distance from outside curve to axis of revolution, r = distance from inside curve to axis of revolution | 72 | |
| 735253561 | length of curve | ∫ √(1 + (dy/dx)²) dx over interval a to b | 73 | |
| 735253562 | L'Hopitals rule | use to find indeterminate limits, find derivative of numerator and denominator separately then evaluate limit | 74 | |
| 735253563 | indeterminate forms | 0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞, 0⁰, ∞⁰ | 75 | |
| 735253564 | 6th degree Taylor Polynomial | polynomial with finite number of terms, largest exponent is 6, find all derivatives up to the 6th derivative | 76 | |
| 735253565 | Taylor series | polynomial with infinite number of terms, includes general term | 77 | |
| 735253566 | nth term test | if terms grow without bound, series diverges | 78 | |
| 735253567 | alternating series test | lim as n approaches zero of general term = 0 and terms decrease, series converges | 79 | |
| 735253568 | converges absolutely | alternating series converges and general term converges with another test | 80 | |
| 735253569 | converges conditionally | alternating series converges and general term diverges with another test | 81 | |
| 735253570 | ratio test | lim as n approaches ∞ of ratio of (n+1) term/nth term > 1, series converges | 82 | |
| 735253571 | find interval of convergence | use ratio test, set > 1 and solve absolute value equations, check endpoints | 83 | |
| 735253572 | find radius of convergence | use ratio test, set > 1 and solve absolute value equations, radius = center - endpoint | 84 | |
| 735253573 | integral test | if integral converges, series converges | 85 | |
| 735253574 | limit comparison test | if lim as n approaches ∞ of ratio of comparison series/general term is positive and finite, then series behaves like comparison series | 86 | |
| 735253575 | geometric series test | general term = a₁r^n, converges if -1 < r < 1 | 87 | |
| 735253576 | p-series test | general term = 1/n^p, converges if p > 1 | 88 | |
| 735253577 | derivative of parametrically defined curve x(t) and y(t) | dy/dx = dy/dt / dx/dt | 89 | |
| 735253578 | second derivative of parametrically defined curve | find first derivative, dy/dx = dy/dt / dx/dt, then find derivative of first derivative, then divide by dx/dt | 90 | |
| 735253579 | length of parametric curve | ∫ √ (dx/dt)² + (dy/dt)² over interval from a to b | 91 | |
| 735253580 | given velocity vectors dx/dt and dy/dt, find speed | √(dx/dt)² + (dy/dt)² not an integral! | 92 | |
| 735253581 | given velocity vectors dx/dt and dy/dt, find total distance travelled | ∫ √ (dx/dt)² + (dy/dt)² over interval from a to b | 93 | |
| 735253582 | area inside polar curve | 1/2 ∫ r² over interval from a to b, find a & b by setting r = 0, solve for theta | 94 | |
| 735253583 | area inside one polar curve and outside another polar curve | 1/2 ∫ R² - r² over interval from a to b, find a & b by setting equations equal, solve for theta. | 95 |
