September 15, 2010
AP Calculus AB Test 2 Review Outline
Section 1.4
Continuity and one-sided limits
a) Definition of continuity
b) Types of discontinuities
c) Existence of a limit
d) Intermediate Value Theorem
Section 1.5
Infinite limits
a) Limit as x approaches c± analytically.
b) Evaluate limit to find vertical asymptote.
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September 15, 2010
Section 3.5
Limits at Infinity
a) Find a limit as x approaches ±∞
analytically.
b) Evaluate the appropriate limit(s) to find
any horizontal asymptote(s) of a function.
c) Find the equation of a slant asymptote.
d) Use the techniques we have learned to
sketch the graph of a rational function.
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September 15, 2010
Write a function f such that f has x = -2 as a
vertical asymptote and y = -4 as a horizontal
asymptote. Then sketch the graph.
Sketch the graph of a function with the
following attributes.
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September 15, 2010
If the limit does not exist explain why.
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September 15, 2010
Section 2.1
If f is defined on an open interval containing
c, and if the limit
lim f(c + ∆x) − f(c) = m
∆x→0
∆x
exists, then the line passing through (c, f(c))
with slope m is the tangent line to the graph
of f at the point (c, f(c)).
Definition of the derivative:
f(x + ∆x) − f(x)
f '(x) = lim
∆x→0
∆x
Alternate definition of the derivative:
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