2 Midterm Review by https://padlet.com/zjeffrey/b2bby4dh0mm1hewg en-us 2022-02-26 22:08:12 UTC 2025-10-22 19:27:37 UTC hello@padlet.com f = kx zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772483 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772483 V = 2pi (integral) radius x height zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772484 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772484 V = 2pi (integral) r(x)*h(x)dx zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772485 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772485 Good to look to use when there is a washer problem in respect to y zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772486 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772486 radius = rotated axis - x zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772487 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772487 height = top - bottom zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772488 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772488 1/b-a zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772489 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772489 1/(b-a) (integral a to b) f(x) dx zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772490 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772490 V = pi (integral) (top - bottom)^2dx zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772491 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772491 disk: pi( integral) radius^2 zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772493 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772493 V = pi (integral) (right - left)^2dy zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772494 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772494 dy = right - left, dx = top - bottom zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772495 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772495 Cross-sections zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772496 Square: A(x) = (top - bottom)^2
Equilateral Triangle: A(x) = sqroot(3)/4(top - bottom)^2
Semi-Circle: A(x) = 1/2pi ((top - bottom)/2)^2]]> 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772496 (cosh)' = (sinh) zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772497 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772497 sinhx = (e^x - e^-x)/2 zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772498 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772498 coshx = (e^x + e^-x)/2 zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772499 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772499 ((sech(x))' = -sech(x)tanh(x) zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772500 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772500 Trig identities cosh^2(x)-sinh^2(x)=1, sech^2(x)+tanh^2(x) = 1 zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772501 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772501 udv = uv - (integral)vdu zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772502 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772502 Log -> Inv Trig -> Algebraic -> Trig -> Expontential zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772503 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772503 LIATE^ zjeffrey https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772505 2022-02-26 22:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2067772505 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091108765 sqrt 1 + (f(x)prime)]]> 2022-03-11 21:09:38 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091108765 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109076 2 pi sqrt 1+ (f(x)prime)

]]> 2022-03-11 21:10:01 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109076 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109263 divergent]]> 2022-03-11 21:10:18 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109263 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109363 convergent]]> 2022-03-11 21:10:26 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109363 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109511 S = 2pi integral r(x) sqrt(1 + dx/dyf(x)^2) dx]]> 2022-03-11 21:10:38 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091109511 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110315 Improper if the integral has a discontinuity or goes to plus/minus infinity]]> 2022-03-11 21:11:48 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110315 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110542 sqrt(a^2 + u^2)
u=atan(x)]]> 2022-03-11 21:12:08 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110542 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110893 sqrt(u^2 - a^2)
u=asec(x)]]> 2022-03-11 21:12:38 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091110893 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091111948 Linear Root: a/(mx+b)]]> 2022-03-11 21:14:03 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091111948 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112019 sqrt(a^2 - u^2)
u=asin(x)]]> 2022-03-11 21:14:09 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112019 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112253 L = integral sqrt(1 + dx/dyf(x)^2) dx]]> 2022-03-11 21:14:29 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112253 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112547 Repeated Linear Root: (a/(mx+b))+(b/(mx+b)^n)]]> 2022-03-11 21:14:56 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091112547 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091113636 Irreducible Quadratic: (ax+b)/(a(x^2)+bx+c)]]> 2022-03-11 21:16:14 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091113636 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091114136 Divergent if there if infinity or negative infinity]]> 2022-03-11 21:16:57 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091114136 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091114263 Convergent if limit exists]]> 2022-03-11 21:17:07 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091114263 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091115061 Repeated Irreducible Quadratic: ((ax+b)/(a(x^2)+bx+c))+((cx+d)/(a(x^2)+bx+c))]]> 2022-03-11 21:18:22 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2091115061 x dx = y dy https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145149801 2022-04-15 20:08:12 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145149801 general solution https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150114 2022-04-15 20:08:51 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150114 particular solution https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150203 2022-04-15 20:09:01 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150203 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150712 The limit of the sequence is the value of the sequence as n approaches infinity]]> 2022-04-15 20:10:14 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150712 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150895 P-test]]> 2022-04-15 20:10:38 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150895 an increases if an<an+1 for all n>=1 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150921 2022-04-15 20:10:41 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145150921 an decreases if an>an+1 for all n>=1 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151169 2022-04-15 20:11:18 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151169 (-1)^n is an alternating factor eliuva https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151488 2022-04-15 20:12:03 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151488 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151497 Geometric series (and their expressions) to evaluate convergence]]> 2022-04-15 20:12:04 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151497 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151629 Integral Test]]> 2022-04-15 20:12:26 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151629 telescoping series https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151729 2022-04-15 20:12:40 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151729 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151808 Direct Comparison Test]]> 2022-04-15 20:12:54 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151808 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151963 Limit Comparison Test]]> 2022-04-15 20:13:09 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145151963 alternating test https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152040 2022-04-15 20:13:21 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152040 absolute convergence https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152090 2022-04-15 20:13:29 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152090 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152233 Ratio Test]]> 2022-04-15 20:13:48 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152233 https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152300 Root Test]]> 2022-04-15 20:13:59 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152300 f(x)=an (x-a)^n https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152459 2022-04-15 20:14:24 UTC https://padlet.com/zjeffrey/b2bby4dh0mm1hewg/wish/2145152459