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A review of various mathematical concepts covered in a final exam, including computing radii and intervals of convergence, estimating roots using taylor polynomials, finding taylor series, evaluating infinite series, working with differential equations, and sketching slope fields. It also includes problems related to population dynamics.
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MATH 106 Final Exam Review, Part II
∑^ ∞
n=
(x + 3)n (5n)(2n)
(a) 1 − 1 + 1/ 2 − 1 /6 + 1/ 24 − 1 /120 + ... (b) 8/ 3 − 8 /9 + 8/ 27 − 8 /81 + ... (c) π − π^3 /6 + π^5 / 120 − ...
(a) Write out the first 3 non-zero terms in the Taylor series about x = 0 for f (x).
(b) Write out the complete series for f (x) in summation notation.
(c) Compute f (13)(0).
(d) Compute lim x→ 0
5 x^5 + f (x) 5 x^9
(a) Write a DE whose solution is P (t), the otter population t years from now.
(b) Find any and all equilibrium solutions.
(c) Find the general solution of your DE.
(d) Find and sketch the particular solution if the current population is 400 otters.
dP dt
=. 001 P (3000 − P ). Sketch solutions for P (t) for the following initial populations: P (0) = 0, P (0) = 100, P (0) = 2000, P (0) = 4000.
See old exams and quizzes at http://abacus.bates.edu/˜etowne/mathresources.html