Calculus Flashcards
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| 3536720417 | 1 |  | 0 | |
| 3536720418 | 0 |  | 1 | |
| 3536720419 | Squeeze Theorem |  | 2 | |
| 3536720420 | f is continuous at x=c if... |  | 3 | |
| 3536720421 | 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 | 4 | |
| 3536720422 | Global Definition of a Derivative |  | 5 | |
| 3536720423 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 6 |
| 3536720424 | nx^(n-1) |  | 7 | |
| 3536720425 | 1 |  | 8 | |
| 3536720426 | cf'(x) |  | 9 | |
| 3536720427 | f'(x)+g'(x) |  | 10 | |
| 3536720428 | The position function OR s(t) |  | 11 | |
| 3536720429 | f'(x)-g'(x) |  | 12 | |
| 3536720430 | uvw'+uv'w+u'vw |  | 13 | |
| 3536720431 | cos(x) |  | 14 | |
| 3536720432 | -sin(x) |  | 15 | |
| 3536720433 | sec²(x) |  | 16 | |
| 3536720434 | -csc²(x) |  | 17 | |
| 3536720435 | sec(x)tan(x) |  | 18 | |
| 3536720436 | dy/dx |  | 19 | |
| 3536720437 | f'(g(x))g'(x) |  | 20 | |
| 3536720438 | 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. | 21 | |
| 3536720439 | 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) | 22 | |
| 3536720440 | 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). | 23 | |
| 3536720441 | 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. |  | 24 |
| 3536720442 | First Derivative Test for local extrema |  | 25 | |
| 3536720443 | Point of inflection at x=k |  | 26 | |
| 3536720444 | 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. |  | 27 |
| 3536720445 | Horizontal Asymptote |  | 28 | |
| 3536720446 | L'Hopital's Rule |  | 29 | |
| 3536720447 | x+c |  | 30 | |
| 3536720448 | sin(x)+C |  | 31 | |
| 3536720449 | -cos(x)+C |  | 32 | |
| 3536720450 | tan(x)+C |  | 33 | |
| 3536720451 | -cot(x)+C |  | 34 | |
| 3536720452 | sec(x)+C |  | 35 | |
| 3536720453 | -csc(x)+C |  | 36 | |
| 3536720454 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 37 |
| 3536720455 | Fundamental Theorem of Calculus #2 |  | 38 | |
| 3536720456 | Mean Value Theorem for integrals or the average value of a functions |  | 39 | |
| 3536720457 | ln(x)+C |  | 40 | |
| 3536720458 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 41 |
| 3536720459 | ln(sinx)+C = -ln(cscx)+C |  | 42 | |
| 3536720460 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | 43 | |
| 3536720461 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | 44 | |
| 3536720462 | If f and g are inverses of each other, g'(x) |  | 45 | |
| 3536720463 | Exponential growth (use N= ) |  | 46 | |
| 3536720464 | Area under a curve |  | 47 | |
| 3536720465 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 48 |
| 3536720466 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 49 |
| 3536720467 | Inverse Secant Antiderivative |  | 50 | |
| 3536720468 | Inverse Tangent Antiderivative |  | 51 | |
| 3536720469 | Inverse Sine Antiderivative |  | 52 | |
| 3536720470 | Derivative of eⁿ |  | 53 | |
| 3536720471 | ln(a)*aⁿ+C |  | 54 | |
| 3536720472 | Derivative of ln(u) |  | 55 | |
| 3536720473 | Antiderivative of f(x) from [a,b] |  | 56 | |
| 3536720474 | Opposite Antiderivatives |  | 57 | |
| 3536720475 | Antiderivative of xⁿ |  | 58 | |
| 3536720476 | Adding or subtracting antiderivatives |  | 59 | |
| 3536720477 | Constants in integrals |  | 60 | |
| 3536720478 | Identity function | D: (-∞,+∞) R: (-∞,+∞) |  | 61 |
| 3536720479 | Squaring function | D: (-∞,+∞) R: (o,+∞) |  | 62 |
| 3536720480 | Cubing function | D: (-∞,+∞) R: (-∞,+∞) |  | 63 |
| 3536720481 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 64 |
| 3536720482 | Square root function | D: (0,+∞) R: (0,+∞) |  | 65 |
| 3536720483 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  | 66 |
| 3536720484 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 67 |
| 3536720485 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 68 |
| 3536720486 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 69 |
| 3536720487 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 70 |
| 3536720488 | Logistic function | D: (-∞,+∞) R: (0, 1) |  | 71 |
| 3536720489 | cos(π/6) | √3/2 | 72 | |
| 3536720490 | cos(π/4) | √2/2 | 73 | |
| 3536720491 | cos(π/3) | 1/2 | 74 | |
| 3536720492 | cos(π/2) | 0 | 75 | |
| 3536720493 | cos(2π/3) | −1/2 | 76 | |
| 3536720494 | cos(3π/4) | −√2/2 | 77 | |
| 3536720495 | cos(5π/6) | −√3/2 | 78 | |
| 3536720496 | cos(π) | −1 | 79 | |
| 3536720497 | cos(7π/6) | −√3/2 | 80 | |
| 3536720498 | cos(5π/4) | −√2/2 | 81 | |
| 3536720499 | cos(4π/3) | −1/2 | 82 | |
| 3536720500 | cos(3π/2) | 0 | 83 | |
| 3536720501 | cos(5π/3) | 1/2 | 84 | |
| 3536720502 | cos(7π/4) | √2/2 | 85 | |
| 3536720503 | cos(11π/6) | √3/2 | 86 | |
| 3536720504 | cos(2π) | 1 | 87 | |
| 3536720505 | sin(π/6) | 1/2 | 88 | |
| 3536720506 | sin(π/4) | √2/2 | 89 | |
| 3536720507 | sin(π/3) | √3/2 | 90 | |
| 3536720508 | sin(π/2) | 1 | 91 | |
| 3536720509 | sin(2π/3) | √3/2 | 92 | |
| 3536720510 | sin(3π/4) | √2/2 | 93 | |
| 3536720511 | sin(5π/6) | 1/2 | 94 | |
| 3536720512 | sin(π) | 0 | 95 | |
| 3536720513 | sin(7π/6) | −1/2 | 96 | |
| 3536720514 | sin(5π/4) | −√2/2 | 97 | |
| 3536720515 | sin(4π/3) | −√3/2 | 98 | |
| 3536720516 | sin(3π/2) | −1 | 99 | |
| 3536720517 | sin(5π/3) | −√3/2 | 100 | |
| 3536720518 | sin(7π/4) | −√2/2 | 101 | |
| 3536720519 | sin(11π/6) | −1/2 | 102 | |
| 3536720520 | sin(2π) | 0 | 103 | |
| 3536720521 | f(x) = e^(x-2) | Asymptote: y=0 Domain: (-∞, ∞) |  | 104 |
| 3536720522 | f(x)=ln(x-2) | Asymptote: x=2 Domain: (2, ∞) |  | 105 |
| 3536720523 | f(x)=ln(-x) | Asymptote: x=0 Domain: (-∞, 0) |  | 106 |
| 3536720524 | f(x)=e^(x+2) | Asymptote: y=0 Domain: (-∞, ∞) |  | 107 |
| 3536720525 | f(x)= -2+lnx | Asymptote: x=0 Domain: (0, ∞) |  | 108 |
| 3536720526 | f(x)=-lnx | Asymptote: x=0 Domain: (0, ∞) |  | 109 |
| 3536720527 | f(x) = e^(x) +2 | Asymptote: y=2 Domain: (-∞, ∞) |  | 110 |
| 3536720528 | f(x)=ln(x+2) | Asymptote: x=-2 Domain: (-2, ∞) |  | 111 |
| 3536720529 | What does the graph y = sin(x) look like? |  | 112 | |
| 3536720530 | What does the graph y = cos(x) look like? |  | 113 | |
| 3536720531 | What does the graph y = tan(x) look like? |  | 114 | |
| 3536720532 | What does the graph y = csc(x) look like? |  | 115 | |
| 3536720533 | What does the graph y = sec(x) look like? |  | 116 | |
| 3536720534 | What does the graph y = cot(x) look like? |  | 117 | |
| 3536720535 | d/dx[e^x]= | e^x | 118 | |
| 3536720536 | d/dx[a^x]= | a^x*lna | 119 | |
| 3536720537 | d/dx[e^g(x)]= | g'(x)e^g(x) | 120 | |
| 3536720538 | d/dx[a^g(x)]= | g'(x)a^g(x)lna | 121 | |
| 3536720539 | d/dx[cos⁻¹x]= | -1/√(1-x^2) | 122 | |
| 3536720540 | d/dx[sin⁻¹x]= | 1/√(1-x^2) | 123 | |
| 3536720541 | d/dx[tan⁻¹x]= | 1/(1+x^2) | 124 | |
| 3536720542 | d/dx[tanx]= | sec²x | 125 | |
| 3536720543 | d/dx[secx]= | secxtanx | 126 | |
| 3536720544 | d/dx[cscx]= | -cscxcotx | 127 | |
| 3536720545 | d/dx[cotx]= | -csc²x | 128 | |
| 3536720546 | ∫e^xdx= | e^x+C | 129 | |
| 3536720547 | ∫a^xdx= | (a^x)/lna+C | 130 | |
| 3536720548 | ∫1/xdx= | ln|x|+C | 131 | |
| 3536720549 | ∫1/(1+x^2)dx= | tan⁻¹x+C | 132 | |
| 3536720550 | ∫1/(a^2+x^2)dx= | (1/a)(tan⁻¹(x/a)+C | 133 | |
| 3536720551 | ∫1/√(1-x^2)dx= | sin⁻¹x+C | 134 | |
| 3536720552 | ∫tanxdx= | ln|secx|+C | 135 | |
| 3536720553 | Trig Identity: 1= | cos²x+sin²x | 136 | |
| 3536720554 | Trig Identity: sec²x= | tan²x+1 | 137 | |
| 3536720555 | Trig Identity: cos²x= | ½(1+cos(2x)) | 138 | |
| 3536720556 | Trig Identity: sin²x= | ½(1-cos(2x)) | 139 | |
| 3536720557 | Trig Identity: sin(2x)= | 2sinxcosx | 140 | |
| 3536720558 | Trig Identity: cos(2x)= | 1-2sin²x = 2cos²x-1 | 141 | |
| 3536720559 | Integration by Parts: Choice of u | I = Inverse Trig Function L = Natural log (lnx) A = Algebraic Expression (x, x², x³...) T = Trig function (sinx, cosx) E = e^x | 142 | |
| 3536720560 | ∫secxdx= | ln|secx+tanx|+C | 143 | |
| 3536720561 | What does the graph y = sin(x) look like? | | 144 | |
| 3536720562 | What does the graph y = cos(x) look like? | | 145 | |
| 3536720563 | What does the graph y = tan(x) look like? | | 146 | |
| 3536720564 | What does the graph y = csc(x) look like? | | 147 | |
| 3536720565 | What does the graph y = sec(x) look like? | | 148 | |
| 3536720566 | What does the graph y = cot(x) look like? | | 149 | |
| 3536720567 | d/dx[e^x]= | e^x | 150 | |
| 3536720568 | d/dx[a^x]= | a^x*lna | 151 | |
| 3536720569 | d/dx[e^g(x)]= | g'(x)e^g(x) | 152 | |
| 3536720570 | d/dx[a^g(x)]= | g'(x)a^g(x)lna | 153 | |
| 3536720571 | d/dx[cos⁻¹x]= | -1/√(1-x^2) | 154 | |
| 3536720572 | d/dx[sin⁻¹x]= | 1/√(1-x^2) | 155 | |
| 3536720573 | d/dx[tan⁻¹x]= | 1/(1+x^2) | 156 | |
| 3536720574 | d/dx[tanx]= | sec²x | 157 | |
| 3536720575 | d/dx[secx]= | secxtanx | 158 | |
| 3536720576 | d/dx[cscx]= | -cscxcotx | 159 | |
| 3536720577 | d/dx[cotx]= | -csc²x | 160 | |
| 3536720578 | ∫e^xdx= | e^x+C | 161 | |
| 3536720579 | ∫a^xdx= | (a^x)/lna+C | 162 | |
| 3536720580 | ∫1/xdx= | ln|x|+C | 163 | |
| 3536720581 | ∫1/(1+x^2)dx= | tan⁻¹x+C | 164 | |
| 3536720582 | ∫1/(a^2+x^2)dx= | (1/a)(tan⁻¹(x/a)+C | 165 | |
| 3536720583 | ∫1/√(1-x^2)dx= | sin⁻¹x+C | 166 | |
| 3536720584 | ∫tanxdx= | ln|secx|+C | 167 | |
| 3536720585 | Trig Identity: 1= | cos²x+sin²x | 168 | |
| 3536720586 | Trig Identity: sec²x= | tan²x+1 | 169 | |
| 3536720587 | Trig Identity: cos²x= | ½(1+cos(2x)) | 170 | |
| 3536720588 | Trig Identity: sin²x= | ½(1-cos(2x)) | 171 | |
| 3536720589 | Trig Identity: sin(2x)= | 2sinxcosx | 172 | |
| 3536720590 | Trig Identity: cos(2x)= | 1-2sin²x = 2cos²x-1 | 173 | |
| 3536720591 | Integration by Parts: Choice of u | I = Inverse Trig Function L = Natural log (lnx) A = Algebraic Expression (x, x², x³...) T = Trig function (sinx, cosx) E = e^x | 174 | |
| 3536720592 | ∫secxdx= | ln|secx+tanx|+C | 175 |