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Need to review more fully: integration by parts, inverse trig derivatives, and mean value theorem
Already mastered: riemann sums and basic free response q's (find velocity/position when given acceleration, when is speed incr/decr, etc) -
Good to remember: y=vx and dy=vdx + xdv
Population growth model: P=pe^kt, solve to get P=M/(1+Ae^(-kt)) -
Need more series/sequence review, look over direct and limit comparison tests
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Remembered Euler's method!
Note: because Euler's method is basically a tangent line approximation, it is an overestimate for a concave down curve and an underestimate for a concave up curve. -
Things to remember: remainder of alternating series= first neglected term, for ratio and root test: lim>1 or lim=infinity means the series is divergent and lim=1 is inconclusive (ratio test usually helpful but always inconclusive for p series)
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Notes from debriefing:
Make answers to 3 decimal points
Revisit inverse trig derivatives
Revisit methods to solving DEs -
Integration by parts is pretty important. u=easier to differentiate, dv=easier to integrate. Remember LIPET.
It's also sometimes helpful to add and subtract something to the numerator to simplify it. -
When finding radius of convergence, use ratio test and check endpoints!
Also, as seen in free response practice, taylor series for cosx or sinx shifts when centeres around pi/2 (so series of cosx around pi/2= series of sinx around 0) -
Disc method= mastered
shell method: 2*pi Integral of f(x)*x dx, representative rectangles parallel to axis that's rotated around -
Not bad. Multiple choice was overall pretty easy. Free response wasn't so simple, #6 didn't go so well. But I'm still feelin a five....
