## . Suppose that, the population of a bacteria colony changes according to P (t)= 8e-0.35t (millions of bacteria ) hour (a) Find a formula for the population as a function of time, P(t) , if there are 9 million of bacteria at t =0 hours . (b) Find the change in population, AP , from t= 1 to ?=4 hours. (c) Find the average population, Pave , from t=1 to t=4 hours.

. Suppose that, the population of a bacteria colony changes according to P (t)= 8e-0.35t (millions of bacteria ) hour (a) Find a formula for the population as a function of time, P(t) , if there are 9 million of bacteria at t =0 hours . (b) Find the change in population, AP , from t= 1 to ?=4 hours. (c) Find the average population, Pave , from t=1 to t=4 hours.

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## 3. Given the function g(x)=4x-4/3. (a) Find the volume of the solid of rotation that results from rotating g(x), ISx <3 about the x-axis. Tal Find the average of g(x) over the interval [1,3] . (c) Evaluate flotx ])dx.

3. Given the function g(x)=4x-4/3.

(a) Find the volume of the solid of rotation that results from rotating g(x), ISx <3 about the x-axis.

Tal Find the average of g(x) over the interval [1,3] .

(c) Evaluate

flotx ])dx.

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## 2. i. Carefully, graph the function f(x, y)=-3x-3y+2 on the first octant of a properly labeled coordinate system. ii. Use a ruler to generate a contour map for the function f(x, y) = Vx – y , using z=0, 1, and 2 . iii. Given f(x,y)=- 3-2x’y log, (2x" 4xy3 -2x? y find f,(x, y) . (Do not simplify.) 3-2x’ y 10g, ( 2×3) iv. Give a point (x, y) where the function f(x, y )=- cannot be evaluated, and state the reason. 4xy3 – 2x’ y

2. i. Carefully, graph the function f(x, y)=-3x-3y+2 on the first octant of a properly labeled coordinate system.

ii. Use a ruler to generate a contour map for the function f(x, y) = Vx – y , using z=0, 1, and 2 .

iii. Given f(x,y)=-

3-2x’y log, (2x"

4xy3 -2x? y

find f,(x, y) . (Do not simplify.)

3-2x’ y 10g, ( 2×3)

iv. Give a point (x, y) where the function f(x, y )=-

cannot be evaluated, and state the reason.

4xy3 – 2x’ y

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## 2. i. Carefully, graph the function f(x, y)=-3x-3y+2 on the first octant of a properly labeled coordinate system. ii. Use a ruler to generate a contour map for the function f(x, y) = Vx – y , using z=0, 1, and 2 . iii. Given f(x,y)=- 3-2x’y log, (2x" 4xy3 -2x? y find f,(x, y) . (Do not simplify.) 3-2x’ y 10g, ( 2×3) iv. Give a point (x, y) where the function f(x, y )=- cannot be evaluated, and state the reason. 4xy3 – 2x’ y

2. i. Carefully, graph the function f(x, y)=-3x-3y+2 on the first octant of a properly labeled coordinate system.

ii. Use a ruler to generate a contour map for the function f(x, y) = Vx – y , using z=0, 1, and 2 .

iii. Given f(x,y)=-

3-2x’y log, (2x"

4xy3 -2x? y

find f,(x, y) . (Do not simplify.)

3-2x’ y 10g, ( 2×3)

iv. Give a point (x, y) where the function f(x, y )=-

cannot be evaluated, and state the reason.

4xy3 – 2x’ y