Exercises
UF Calculus Set 9
1. Find the points at which the graph below is (a) discontinuous (b) right continuous only (c)
left continuous only. Classify each point of discontinuity as removable (hole), jump, or inﬁnite
(vertical asymptote).
2. Discuss the continuity of the functions described below. What type of discontinuity does each
have? Refer to the ﬁgure for parts (a) and (b) .
(a) the angle of elevation you make with your eyes in order to see the top of a ﬂagpole if
you are standing at position
x
on a number line, and the ﬂagpole is at position 0.
(b) the slope of your line of sight to the top of the ﬂagpole when standing at position
x
on a
number line, in the situation described above.
(c) the vertical distance
D
from your hand to the nearest object as you move it horizontally
across your desk and over a textbook (see lecture 3, problem 3 for an illustration)
3. Evaluate the limits stepbystep, using limit laws and the continuity of the functions involved.
(a)
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 Spring '08
 ALL
 Calculus, Geometry, Continuity, Continuous function, lim ln x→2

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