Calculus Formulas
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| 167205412 | lim (x->0) sinx/x | 1 | |
| 167205413 | lim (x->0) cosx-1/x | 0 | |
| 167205414 | continuity terms | 1. f(c) exists 2. lim (x->c) f(x) exists 3. lim (x->c) f(x) = f(c) | |
| 167205415 | jump discontinuity | curve "breaks: and starts somewhere else (left limit doesn't equal right limit) | |
| 167205416 | point discontinuity | curve has a "hole" (limit as x approaches a ≠ f at a) | |
| 167205417 | essential discontinuity | curve has a vertical asymptote | |
| 167205418 | removable discontinuity | rational expression w/ common factors that cancel out | |
| 167205419 | tangent line | touches curve at exactly one point | |
| 167205420 | derivative | lim (h->0) f(x1+h) - f(x1) / h | |
| 167205421 | d/dx sinx | cosx | |
| 167205422 | d/dx cosx | -sinx | |
| 167205423 | d/dx tanx | sec^2x | |
| 167205424 | d/dx cotx | -csc^2x | |
| 167205425 | d/dx secx | secxtanx | |
| 167205426 | d/dx cscx | -cscxcotx | |
| 167205427 | Area of trapezoid | 1/2 (b1+b2)(h) | |
| 167205428 | Volume of cylinder | πr^2h | |
| 167205429 | surface area of cyclinder | 2πrh | |
| 167205430 | volume of cone | 1/3πr^2h | |
| 167205431 | volume of sphere | 4/3πr^3 | |
| 167205432 | surface area of sphere | 4πr^3 | |
| 167205433 | mean value theorem for derivatives | f'(c) = f(b)-f(a)/b-a | |
| 167205434 | rolle's theorem | 1. continuous on [a,b] 2. differentiable on (a,b) 3. f(a) = f(b) = 0 THEN there is one c between a and b that f'(c) = 0 | |
| 167205435 | semicircle | y = root(r^2 - x^2) | |
| 167205436 | position | x(t) | |
| 167205437 | velocity | x'(t) | |
| 167205438 | acceleration | x''(t) | |
| 167205439 | d/dx lnu | 1/u du/dx | |
| 167205440 | d/dx e^u | e^u du/dx | |
| 167205441 | d/dx logau | 1/u lna du/dx | |
| 167205442 | d/dx a^u | a^u (lna) du/dx | |
| 167205443 | ∫du/u | ln|u|+C | |
| 167205444 | ∫tanx | -ln|cosx|+C | |
| 167205445 | ∫cotx | ln|sinx|+C | |
| 167205446 | ∫secx | ln|secx+tanx| + C | |
| 167205447 | ∫cscx | -ln|cscx+cotx| | |
| 167205448 | ∫a^u | 1/lna a^u + C | |
| 167205449 | L'hopital's rule | lim (x->c) f(x)/g(x) = f'(x)/g'(x) only for indeterminate functions (equal 0/0 or ∞/∞) so basically solve them separately | |
| 167205450 | trapezoid rule | b-a/2n [f(xo) + 2f(x1) + 2f(x2) ... f(xn)} | |
| 167205451 | simpson's rule | b-a/3n [f(xo) + 4f(x1) + 2f(x2) + 4f(x3) .... f(xn)] | |
| 167205452 | Mean value theorem for integrals | f(c) = 1/b-a ∫[a to b] f(x)dx | |
| 167205453 | Second fundamental theorem | dF/dx=d/dx ∫[a to x] f(t)dt = f(x) | |
| 167205454 | Volume of disk | π (radius) ^2 (thickness) | |
| 167205455 | Volume of washer | π [(outer r)^2 - (inner r)^2] (thickness) | |
| 167205456 | Volume of shell | 2π (radius) (altitude) (thickness) | |
| 167205457 | ∫udv aka integration by parts | uv-∫vdu |