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Integration Review
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) -
Differential Equation Review
Good to remember: y=vx and dy=vdx + xdv
Population growth model: P=pe^kt, solve to get P=M/(1+Ae^(-kt)) -
Practice Multiple Choice 1
Need more series/sequence review, look over direct and limit comparison tests -
Practice Multiple Choice 2
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. -
Series and Sequence Review
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) -
Practice Test Debrief
Notes from debriefing:
Make answers to 3 decimal points
Revisit inverse trig derivatives
Revisit methods to solving DEs -
Integration Techniques
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. -
Infinite Series review
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) -
Volume Review
Disc method= mastered
shell method: 2*pi Integral of f(x)*x dx, representative rectangles parallel to axis that's rotated around -
The Big Game
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....
