2 Testing Algorithms for Weather Prediction (16

points)

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Exciting news from the town of Magitek, ON: the city council has invested

$1.4M in the installation and deployment of a new weather center with Temp-

Sim temperature simulation technology. By using new algorithms developed by

top scientists, TempSim claims to offer weather prediction data with accuracy

"limited only by how precise you want it to be." The fine print states that

they are claiming that accuracy will always improve, without bound, as better

parameters are provided.

In order to verify these claims, the Magitek city council has hired consult-

ing firm Extodout to independently test the TempSim system. Extodout has

measured the resulting °C error (E) in temperature prediction for temperatures

one week into the future, based on the resolutions of spatial and temporal data,

which are given by the distance steps in kilometers and time step in minutes,

respectively.

TempSim has provided three algorithms for temperature prediction; choice

of algorithm depends on the general climate of the region and is to be determined

empirically. You are a city council member reviewing Extodout's measurements

and trying to decide which algorithm to program into the Magitek, ON weather

system. Note: the domains for these functions require s> 0 and t> 0.

(a) (5 points) Algorithm A has an error in prediction bounded by the following

equation:

3st

(s+21)2

Does this function have a limit as (s, t) → (0,0)? If so, what is it?

E =