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MATH 231 - Scientific Calculus I
Evaluating Limits for Functions Given by Formula
Recall that we have organized the function formulas for this course as falling into one of two categories:
the Basic Three
the Five Ways that functions are built from the Basic Three
With this organization in mind, it is easy to list out the properties of limits (known as the Limit Laws that
we will need to evaluate limits in this course. Here are the Limit Laws, for each of these categories:
the Basic Three
Exponential Functions f(t)=b
t
, where b is a positive constant.
lim
t?c
f(t)=f(c).
Trig Functions f(t)=sin(t)andg(t)=cos(t).
lim
t?c
f(t)=f(c) and lim
t?c
g(t)=g(c)
Power Functions f(t)=t
p
, where p is a constant.
lim
t?c
f(t)=f(c), provided the domain of f contains an open interval which includes c.
Functions built from the Basic Three
Arithmetic Combinations: Example: Addition. (The others are similar, and are listed on page 108 of
our text.) If lim
t?c
f(t) and lim
t?c
g(t) both exi...

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