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Calc
| Term | Definition |
|---|---|
| Half angle formulas | sin^2x =1/2(1-cos2x) cos^2x = 1/2(1 +cos2x) |
| If sin^mx or cos^nx are odd | separate, use trig identities, then u sub |
| If both sin^mx and cos^nx are even | use half formulas |
| Basic trig identity | cos^2x + sin^2x = 1 |
| Complex trig identity | tan^2x + 1 =sec^2x |
| If tan^mx is odd or sec^nx is even | separate, use trig identities, then u sub |
| If tan^mx is even or sec^nx is odd | use integration by parts |
| Tan | m |
| Sec | n |
| Cos | n |
| Sin | m |
| Int of sin(mx)cos(nx)dx | sinAcosB = 1/2(sin(A-B) + sin(A+)) |
| int of sin(mx)sin(nx)dx | sinAsinB = 1/2(cos(A-B) - cos(A+B)) |
| int of cos(mx)cos(nx)dx | cosAcosB = 1/2(cos(A-B) + cos(A+B)) |
| Double angle formula | sin(theta)cos(theta) = 1/2sin2(theta) |
| sq(a^2 - x^2) | x = asin(theta) |
| sq(a^2 + x^2) | x = atan(theta) |
| sq(x^2 - a^2) | x = asec(theta) |
| int sinx^2 | (1-cos2theta)/2 |
| int cosx^2 | (1+cos2theta)/2 |
| int 1/(x^2+a^2)dx | 1/a(tan^-1(x/a)) |
| int from 1 infinity (1/x^p)dx | convergent if p >1 divergent if p<= 1 |
| Before solving improper integrals | check for discontinuity |
| Comparison test | f(x)>=g(x) for all x>=a |
| Comparison test: convergence | if f(x) is convergent than automatically g(x) is |
| Comparison test: divergence | if g(x) is divergent than automatically f(x) is |
| Limits of sequences | if the lim as n goes to infinity of an = L than an converges to L if the lim as n goes to infinity of an = -+infinity than an diverges |
| Function method | if lim of f(x) converges so does lim of an if lim of f(x) diverges so does lim of an |
| Absolute value theory | if the lim as n goes to infinity of the abs val of an = 0 than the lim as n goes to infinity of an = 0 |
| Important sequence | if the lim as n goes to infinity of abs val of r < 1 = 0 if the abs val of r is > 1 then = infinity |
| Squeeze theorem | an =< bn =< cn for all of n if the lim of an as n goes to infinity = the lim of cn as n goes to infinity = L then the lim of bn as n goes to infinity = L |
| Monotone sequences | increasing when an <= an+1 decreasing when an>=an+1 |
| For geometric sequences (a-ar^n)/(1-r) | if abs val of r < 1 than it converges if abs val of r > 1 than it diverges |
| Geometric series if n = 1 | a(r)/1-r |
| Geometric serum if n = 0 | a/1-r |
Created by:
user-1973161