Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Solution Summary: The author explains the base-change property for logarithmic functions, which is mathematically expressed as mathrmlog_ba=
Use a graphing utility and the change-of-base properly to graph
y
=
log
3
x
,
y
=
log
25
x
, and
y
=
log
100
x
in the same viewing rectangle.
a. Which graph is on the top in the interval (0,1)? Which is on the bottom?
b. Which graph is on the lop in the interval (1,
∞
)? Which is on the bottom?
c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using
y
=
log
b
x
where b > 1.
Disprove each statement in Exercises 116-120 by
a.letting y equal a positive constant of your choice, and
b.using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
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