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Calculus Terms
| Term | Definition |
|---|---|
| lim x->0 sinx/x | 1 |
| lim x->0 (1-cosx)/x | 0 |
| lim x->0 tanx/x | 1 |
| lim x->0 x/(1-cosx) | DNE |
| sin2Θ | 2sinΘcosΘ |
| lim h->0 (f(x+h)-f(x))/h | f'(x) |
| d/dx cu | cu' |
| d/dx u +- v | u' +- v' |
| d/dx uv | u'v + uv' |
| d/dx u/v | (u'v - uv')/v^2 |
| d/dx c | 0 |
| d/dx u^n | nu^(n-1)u' |
| d/dx x | 1 |
| d/dx |u| | u/|u| (u') |
| d/dx lnu | u'/u |
| d/dx e^u | e^(u) u' |
| d/dx loga(u) | u'/(lna)u |
| d/dx a^u | (lna)a^(u) u' |
| d/dx sinu | (cosu) u' |
| d/dx cosu | (-sinu) u' |
| d/dx tanu | (sec^2u)u' |
| d/dx cotu | -(csc^2u)u' |
| d/dx cscu | (-cscucotu)u' |
| d/dx secu | (secutanu)u' |
| d/dx arcsinu | u'/√(1-u^2) |
| d/dx arccosu | -u'/√(1-u^2) |
| d/dx arccotu | -u'/(1+u^2) |
| d/dx arctanu | u'/(1+u^2) |
| d/dx arccscu | -u'/(|u|√(u^2-1)) |
| d/dx arcsecu | u'/(|u|√(u^2-1)) |
| ∫du/u | ln|u| + C |
| ∫e^u du | e^u + C |
| ∫a^u du | a^u/(lna) + C |
| ∫x^u du | (x^u+1)/u+1 + C |
| ∫sinu du | -cosu + C |
| ∫cosu du | sinu + C |
| ∫tanu du | ln|secu| + C |
| ∫cotu du | ln|sinu| + C |
| ∫secu du | ln|secu + tanu| + C |
| ∫cscu du | -ln|cscu + cotu| + C |
| ∫secutanu du | secu + C |
| ∫cscucotu du | -cscu + C |
| ∫sec^2u du | tanu + C |
| ∫csc^2u du | -cotu + C |
| ∫1/√(a^2 - u^2) du | 1/a arcsin u/a + C |
| ∫du/a^2 + u^2 | 1/a arctan u/a + C |
| ∫1/u√(u^2 - a^2) du | 1/a arcsec |u/a| + C |
| if F(x) = f(g(x)), then F'(x) = | f'(g(x))g'(x) |
| loga(b) | lnb/lna |
| cone volume | 1/3πr²h |
| sphere surface area | 4πr² |
| cylinder volume | πr²h |
| sphere volume | (4/3)πr³ |
| lim n->∞ (1 + 1/n)^n | e |
| lim n->∞ (1+x/n)^n | e^x |
| trapezoid area | 1/2h(b1+b2) |
| Average value of f(x) over [a,b] | 1/(b-a) ∫f(x) dx |
| ∫udv | uv - ∫vdu |
| ∫lnx dx | xlnx - x + C |
| sin^2Θ | (1-cos2Θ)/2 |
| cos^2Θ | (1+cos2Θ)/2 |
| tan^2Θ | (1-cos2Θ)/(1+cos2Θ) |
Created by:
noahboah
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