1. L(x, y) = -2.83 + 0.14x + 1.91y L(x, y) = -2.83 + 1.41x + 1.41y
Find the linearization L(x, y) of the function at the given point. {image} Select the correct answer (rounded to the nearest hundredth):
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y
L(x, y) = x y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Use the linearization L(x, y) of the function {image} at (5, 3, -3) to approximate f(4.95, 3.2, -2.89). Select the correct answer (rounded to the nearest hundredth): 1.
f(4.95, 3.2, -2.89) {image} 6.56
f(4.95, 3.2, -2.89) {image} 6.44
f(4.95, 3.2, -2.89) {image} 7.09
f(4.95, 3.2, -2.89) {image} 6.47
f(4.95, 3.2, -2.89) {image} 7.27
f(4.95, 3.2, -2.89) {image} 6.49 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Find the differential of the function. {image}1.
{image} 2. 3. 4. 5. 6. 7. 8. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Use differentials to estimate the amount of tin in a closed tin can with diameter 10 cm and height 11 cm if the tin is 0.01 cm thick. Select the correct answer (rounded to the nearest hundredth):
{image} 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV = 8.31T where P is measured in kilopascals, V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure if the volume changes from 12 L to 11 L and the temperature changes from 310 K to 306 K.
{image} 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50