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|?

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

2 liters for 10   people

step-by-step explanation: