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Cells - Calculus Two for Biological Sciences - Exam, Exams of Calculus

Guru Angad Dev Veterinary and Animal Sciences UniversityCalculus

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

Typology: Exams

2012/2013

Uploaded on 02/18/2013

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Math 30: Unit 3 Exam
Fall Semester 2006
1. (8 points) You model the population Pof cells growing in culture as a function of time by
the equation
dP
dt =0.1P.
At time t=1, we count 100 cells. Give a formula for the number of cells at t=0.
2. (8 points) For a function f(x), its two-term Taylor approximation about x=x0is given by
f(x)≈f(x0) + (x−x0)f′(x0) + 1
2! f′′ (x0) + 1
3! f′′′(x0) + ··· .
Find the two non-zero terms of the Taylor approximation for f(x) = e−xabout x=0.
pf2

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Math 30: Unit 3 Exam

Fall Semester 2006

  1. (8 points) You model the population P of cells growing in culture as a function of time by the equation dP dt

= 0.1P.

At time t = 1, we count 100 cells. Give a formula for the number of cells at t = 0.

  1. (8 points) For a function f (x), its two-term Taylor approximation about x = x 0 is given by

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.

  1. (8 points) Consider the differential equation

du dt

= f (u)

with the graph of f (u) given below.

u

f(u)

u 0

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.