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This is the Exam of Calculus Two for Biological Sciences which includes Numerical Sum, Approximation, Midpoint Rule, Terms, Modeled, Type Equilibrium Points, Starting Population etc. Key important points are: Cells, Population, Culture, Function, Number of Cells, Taylor Approximation, Two Term, Non Zero Terms, Differential Equation, Graph
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Fall Semester 2006
At time t = 1, we count 100 cells. Give a formula for the number of cells at t = 0.
f (x) ≈ f (x 0 ) + (x − x 0 ) f ′(x 0 ) +
f ′′(x 0 ) +
f ′′′(x 0 ) + · · ·.
Find the two non-zero terms of the Taylor approximation for f (x) = e−x^ about x = 0.
du dt
= f (u)
with the graph of f (u) given below.
Analyze this differential equation graphically. Identify, label and classify all of its equilib- rium points directly on the graph above. Using that information, describe the long-time behavior of the solution when u( 0 ) = u 0.