Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is 1 hr 35 m. Suppose rangers log the first eruption on a given day at 12 : 57 am. Using a 1 = 57 , write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight. At what time of day (e.g., 7 : 15 am) is the 10 th eruption expected to occur? At what time of day is the last eruption expected to occur?
Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is 1 hr 35 m. Suppose rangers log the first eruption on a given day at 12 : 57 am. Using a 1 = 57 , write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight. At what time of day (e.g., 7 : 15 am) is the 10 th eruption expected to occur? At what time of day is the last eruption expected to occur?
Solution Summary: The author explains the formula for sequence of eruptions times that day in terms of number of minutes after midnight, if the first eruption is at a_1=57, and the average time between eruption
Old Faithful Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicated that the average time between eruptions is
1
hr
35
m.
Suppose rangers log the first eruption on a given day at
12
:
57
am. Using
a
1
=
57
, write a prediction formula for the sequence of eruption times that day in terms of the number of minutes after midnight.
At what time of day (e.g.,
7
:
15
am) is the
10
th eruption expected to occur?
At what time of day is the last eruption expected to occur?
A graph of the function f is given below:
Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1
Of is defined at a.
If is not defined at x = a.
Of is continuous at x = a.
If is discontinuous at x = a.
Of is smooth at x = a.
Of is not smooth at = a.
If has a horizontal tangent line at = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
If has no tangent line at x = a.
f(a + h) - f(a)
lim
is finite.
h→0
h
f(a + h) - f(a)
lim
h->0+
and lim
h
h->0-
f(a + h) - f(a)
h
are infinite.
lim
does not exist.
h→0
f(a+h) - f(a)
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
The graph below is the function f(z)
4
3
-2
-1
-1
1
2
3
-3
Consider the function f whose graph is given above.
(A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter
"DNE". If a limit can be represented by -∞o or ∞o, then do so.
lim f(z)
+3
lim f(z)
1-1
lim f(z)
f(1)
= 2
=
-4
= undefined
lim f(z) 1
2-1
lim f(z):
2-1+
lim f(x)
2+1
-00
= -2
= DNE
f(-1) = -2
lim f(z) = -2
1-4
lim f(z)
2-4°
00
f'(0)
f'(2)
=
=
(B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left-
continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If
there are none, enter "none".
Discontinuous at z =
Left-continuous at x =
Invalid use of a comma.syntax incomplete.
Right-continuous at z =
Invalid use of a comma.syntax incomplete.
(C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list,
if needed (eg. -2, 3, 5).…
A graph of the function f is given below:
Study the graph of f at the value given below. Select each of the following that applies for the value
a = -4.
f is defined at = a.
f is not defined at 2 = a.
If is continuous at x = a.
Of is discontinuous at x = a.
Of is smooth at x = a.
f is not smooth at x = a.
If has a horizontal tangent line at x = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
Of has no tangent line at x = a.
f(a + h) − f(a)
h
lim
is finite.
h→0
f(a + h) - f(a)
lim
is infinite.
h→0
h
f(a + h) - f(a)
lim
does not exist.
h→0
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
Chapter 12 Solutions
Mylab Math With Pearson Etext -- Standalone Access Card -- For Precalculus (11th Edition)
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