The sandwich theorem for functions of two variables states that if g(x, y)≤f(x, y)≤h(x, y) for all (x, y)≠(x0,y0)
in a disk centered at
(x0,y0)
and if g and h have the same finite limit L as
(x, y)→(x0,y0)
then
lim(x, y)→(x0,y0)f(x, y)=L.
Use this result to support your answers to the question. Does knowing that
2|xy|−x2y26<4−4cos|xy|−−−√<2| xy|
2 | x y | - \frac { x ^ { 2 } y ^ { 2 } } { 6 } < 4 - 4 \cos \sqrt { | x y | } < 2 | x y | tell you anything about
lim(x, y)→(0,0)4−4cos|xy|−−−√|xy|?

hiking down a winding trail.

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

all three statements are true

step-by-step explanation:

a shipping fee of 5% is charged online with every item purchased online

first let's just take each option and calculate them based on this, to see if the answers matched

keith buys a 40 dollar book

40 x 0.05 = 2

therefore there will be a two dollar fee on keith's book

40 + 2 =42

the first statement is true

a chair costs $80

80 x 0.05 = 4

80 + 4 = 84

the second statement is true

george buys a 20 dollar calculator

20 x 0.05 = 1

20 + 1 = 21

the third statements are true

all three statements are true