Calculus Flashcards
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| 5811122275 | f is continuous at x=c if... |  | 0 | |
| 5811122276 | 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 | 1 | |
| 5811122277 | Global Definition of a Derivative |  | 2 | |
| 5811122278 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 3 |
| 5811122279 | nx^(n-1) |  | 4 | |
| 5811122280 | 1 |  | 5 | |
| 5811122281 | cf'(x) |  | 6 | |
| 5811122282 | f'(x)+g'(x) |  | 7 | |
| 5811122283 | f'(x)-g'(x) |  | 8 | |
| 5811122284 | cos(x) |  | 9 | |
| 5811122285 | -sin(x) |  | 10 | |
| 5811122286 | sec²(x) |  | 11 | |
| 5811122287 | -csc²(x) |  | 12 | |
| 5811122288 | sec(x)tan(x) |  | 13 | |
| 5811122289 | f'(g(x))g'(x) |  | 14 | |
| 5811122290 | 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. | 15 | |
| 5811122291 | 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. |  | 16 |
| 5811122292 | Horizontal Asymptote |  | 17 | |
| 5811122293 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 18 |
| 5811122294 | Square root function | D: (0,+∞) R: (0,+∞) |  | 19 |
| 5811122295 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  | 20 |
| 5811122296 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 21 |
| 5811122297 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 22 |
| 5811122298 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 23 |
| 5811122299 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 24 |
| 5811122301 | √3/2 | cos(π/6) | 25 | |
| 5811122302 | √2/2 | cos(π/4) | 26 | |
| 5811122303 | 1/2 | cos(π/3) | 27 | |
| 5811122308 | -1 | cos(π) | 28 | |
| 5811122309 | −√3/2 | cos(7π/6) | 29 | |
| 5811122310 | −√2/2 | cos(5π/4) | 30 | |
| 5811122311 | −1/2 | cos(4π/3) | 31 | |
| 5811122312 | 0 | cos(3π/2) | 32 | |
| 5811122333 | What does the graph y = sin(x) look like? |  | 33 | |
| 5811122334 | What does the graph y = cos(x) look like? |  | 34 | |
| 5811122335 | What does the graph y = tan(x) look like? |  | 35 | |
| 5811122337 | d/dx[tanx]= | sec²x | 36 | |
| 5811122338 | d/dx[secx]= | secxtanx | 37 | |
| 5811122339 | d/dx[cscx]= | -cscxcotx | 38 | |
| 5811122340 | d/dx[cotx]= | -csc²x | 39 | |
| 5811122341 | Trig Identity: 1= | cos²x+sin²x | 40 | |
| 5811122351 | d/dx[uv]= | vu'+uv' | 41 | |
| 5811122352 | d/dx[u/v]= | (vu'-uv')/v^2 | 42 | |
| 5811122353 | d/dt[s(t)]= | v(t) | 43 | |
| 5811122354 | d/dt[v(t)]= | a(t) | 44 | |
| 5811122355 | Average Velocity | (Change in Position)/(Change in Time) | 45 | |
| 5811122356 | Average Acceleration | (Change in Velocity)/(Change in Time) | 46 | |
| 5811122357 | When is a object stopped? | v(t) = 0 | 47 | |
| 5811122358 | When is an object moving left? | v(t) < 0 | 48 | |
| 5811122359 | When is an object moving right? | v(t) > 0 | 49 | |
| 5811122360 | When is an object speeding up? | a(t) and v(t) have same sign | 50 | |
| 5811122361 | When is an object slowing down? | a(t) and v(t) have different signs | 51 | |
| 5811122362 | When does an object change direction? | v(t) changes sign | 52 | |
| 5811122363 | vu'+uv' | Product Rule | 53 | |
| 5811122364 | lo dhi minus hi dlo over lolo | Quotient Rule | 54 | |
| 5811122365 | s(b) - s(a) | Displacement | 55 | |
| 5811122366 | [s(b)-s(a)] / (b - a) | Average Velocity | 56 |