MATH 1200 Study Guide - Final Guide: Asymptote, Product Rule, Constant FunctionPremium
4 pages121 viewsFall 2016
SchoolUniversity of Guelph
Course CodeMATH 1200
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MATH 1200 8 Dec 2016
A tangent line is a line that locally touches a function at only one point. To ﬁnd the slope of a tangent line, at a
given point a:
Anormal line is the line perpendicular to the tangent; they have a slope of −1/m.
Assuming that limx→af(x)and limx→ag(x)both exist, where a, c ∈R.
1. limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)
2. limx→acf(x) = c·limx→af(x)
3. limx→af(x)g(x) = limx→af(x)·limx→ag(x)
5. limx→ah(f(x)) = h(limx→af(x)), for h(x)continuous.
If f(p) = 0 for any polynomial f(x),(x−p)is a factor of f(x).
Ex. Find limx→2
2x4+ 17x3+ 31x2−62x−168
6x5+ 5x4−153x3+ 8x2+ 660x−400.
If you directly substitute x= 2 into the above function, you get 0
0. This means that (x−2) is a factor for
both polynomials in the function. Factor (x−2) out of each polynomial, using synthetic division, then try direct
Functions can sometimes be discontinuous at certain points, this is especially true for piece-wise functions. A limit
exists only when a function is continuous, this is determined by evaluating a limit approaching xfrom both the left
limx→a−f(x) = L−means the limit of f(x)approaching xfrom the left.
limx→a+f(x) = L+means the limit of f(x)approaching xfrom the right.
If L−̸=L+, the limit doesn’t exist.
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