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1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step sizes h = 1 and h = 0:5 (and two different colors).
2. Newton’s Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose you have just poured a cup of coffee with temperature 95 C in a room where the temperature is 20 C. Using Newton’s law, write a differential equation for the temperature of the coffee as a function of time. What is the initial condition?
(x+y+1)dy/dx=1
Write down the system of differential equations for mass system and the spring above. Solution To assist us out let's first take a rapid look at a situation wherein both of
Recognizes the absolute extrema & relative extrema for the given function. f ( x ) = x 2 on [-2, 2] Solution Following is the graph for this fun
Determine the inverse transform of each of the subsequent. (a) F(s) = (6/s) - (1/(s - 8)) + (4 /(s -3)) (b) H(s) = (19/(s+2)) - (1/(3s - 5)) + (7/s 2 ) (c) F(s) =
-2+-9
A Class 4 teacher was going to teach her class fractions. At the beginning of the term she asked the children, "If you had three chocolates, and wanted to divide them equally among
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
I need to come up with a PR plan for a fictitious women''s softball team. How much would something like that cost?
Absolute Convergence While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any
Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 . Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co
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