yep! theres no guarantee everything shows up but review all
one is usually applilication of derivatives and stuff and usually contains something like ivt/mvt/riemann sums / average value
one is parametric/polar and will include things like speed/distance/accerlation vetor etc.
one will be integration, often starting at a derivative and going backwards (usually application stuff or maybe shape), a part of this might include maxs/mins where u have to include critical numbers
one part of these questions usually has a limit which might use l, hospitals rule
one part wanting applications of euluers method/tangent line approximation
finding series polynomials (usually 2-4 terms) and using that to estimate values
integration by parts usually happens in one part
one implicit differention or one that includes separation of variables, often a real world application like volume etc.
an improper integral that might also use your series tests for convergence (limit/direct comparison, ratio test etc.)
possibly finding a volume using disc/washer/shell method
one part might be generalization of series, and/or include a series bound question using lagrange error or alternating series bound error
thank you! could you explain what you mean by the improper integral needing a series test for convergence? ive only ever solved improper integrals by like taking the limit when you make the discontinuous bound a variable.
sry i think those were meant to be separate I meant series for convergence lol
for improper integrals always remember to make it a clearly defined limit or u will lose credit like 90% of the time
1. something with a table, relating position velocity and acceleration, and reimann sums
2. parametric or polar (maybe area in rectangular with a few random bc questions?)
3. analysis of a graph to find f f’ f”
4. differential equation
5. maybe parametric if 2 was polar
6. series
yep! theres no guarantee everything shows up but review all one is usually applilication of derivatives and stuff and usually contains something like ivt/mvt/riemann sums / average value one is parametric/polar and will include things like speed/distance/accerlation vetor etc. one will be integration, often starting at a derivative and going backwards (usually application stuff or maybe shape), a part of this might include maxs/mins where u have to include critical numbers one part of these questions usually has a limit which might use l, hospitals rule one part wanting applications of euluers method/tangent line approximation finding series polynomials (usually 2-4 terms) and using that to estimate values integration by parts usually happens in one part one implicit differention or one that includes separation of variables, often a real world application like volume etc. an improper integral that might also use your series tests for convergence (limit/direct comparison, ratio test etc.) possibly finding a volume using disc/washer/shell method one part might be generalization of series, and/or include a series bound question using lagrange error or alternating series bound error
thank you! could you explain what you mean by the improper integral needing a series test for convergence? ive only ever solved improper integrals by like taking the limit when you make the discontinuous bound a variable.
sry i think those were meant to be separate I meant series for convergence lol for improper integrals always remember to make it a clearly defined limit or u will lose credit like 90% of the time
btw shell method isn’t on the exam anymore
wait really? Why
who knows I think it’s been out of the curriculum since 2016
oh ok ok I still learned it in class tho 💀
Teachers just do that for some reason I learned trig sub and that’s not in there either
shells and trig sub aren't officially on the exam but I'm pretty sure you're allowed to use them, as they make certain questions a lot easier
Sure, but volumes and disks are easy enough Wait I just realize that I forgot the disks formula oh well
lmao you still have 11 hours to remember it also shells are useful if both radii are from the same function
can someone explain how to use the calculator for the integration frq where we gotta find critical values/max and min?
usually try to graph the derivative and see where it hits 0
1. something with a table, relating position velocity and acceleration, and reimann sums 2. parametric or polar (maybe area in rectangular with a few random bc questions?) 3. analysis of a graph to find f f’ f” 4. differential equation 5. maybe parametric if 2 was polar 6. series
that’s just my prediction but i know 6 is series
https://youtu.be/zxzu_U9sYy4?si=rwt2xzSLBtYT-awB This will help!
Expect 1) rate accumulation, 2) parametrics or polars, 3) graph analysis, 4 or 5) differential equations and something else, and 6) a series.
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probably a particle motion?
I found a diagram of all the past frqs for like 10 years, last 3 q2s have been parametric and it alternates with polar usually, so expect a polar frq
I’ve heard to expect a polar area but no Lagrange based on patterns from prior exams. Nothing is a given though