Chapter 1: Limits and Continuity
1.1 Examples of Velocity, Growth Rate, and Area
Average Velocity =
Change of Position
Amount of Time
Instantaneous Velocity=
lim
f(t+h) – f(t)
h>0
h
Average Rate of Growth= Change in Growth
= slope of line joining the points of
Time
the graph
instantaneous Growth: measure average rates of change over shorter times and
a tangent line is drawn and the slope of that line is found
1.2 Limits of Functions
Limit: If f(x) is defined for all x near a, except possibly at a itself, an if we can
ensure that f(x) is as close as we want to L by taking x close enough to a, but not
equal to a, we say that the function f approaches the limit L as x approaches a
Lim
f(x)
= L
x>a
left limit: if f(x) is defined on some interval (b,a) extending to the left of x=a, and
if we can ensure that f(x) is as close as we want to L by taking x to the left of a
and close enough to a, then we say f(x) has left limit L at x=a
right limit: if f(x) is defined on some interval (a,b) extending to the right of x=a,
and if we can ensure that f(x) is as close as we want to L by taking x to the right
of a and close enough to a, then we say f(x) has right limit L at x=a.
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 '10
 IDK
 Calculus, Topology, Continuity, Continuous function, Limit of a function, Instantaneous Velocity= lim

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