Reference no: EM132750969

Question 1 - Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim t→0 (3/t A????1 3/t(^2) +2 ) 12. .Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim t→0 (1/t SQRT(1+t) -(1/t) 13. Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→4 SQRT (x(^2)+9)-5 / x+4 16. Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0? (4/x A????1 4/ (absolute value of x).

Question 2 - Let S be the surface of the region bounded by the coordinate planes and the planes x + 2z = 4 and y = 2. Use the Divergence Theorem to the flux of F(x,y,z) = (2xz)i + (xyz)j + (yz)k through S.

Question 3 - Consider the function f (x, y) = xy + 2. Draw the level sets f = c for c = 1, 2, 3. On the same graph, sketch the gradient vector fields Vf at the points (0, -1), (1, 1), and (-1, 1). [Point to ponder: what is the shape of the graph of PI].

Question 4 - Assume that the x-axis runs west to east and the y-axis runs south to north. Assume that the temperature on a stove is described by the following function: 0(x, y) = 1.5y + -x2 + 1 + 100. Throughout, x and y are measured in centimetre, and 0 is measured in Celsius. (1) A bug at (1, -2) is crawling southeast at the speed 4 cm I sec. How fast is the temperature experienced by the bug changing? (2) If this bug wanted to move in the direction in which the temperature decreases the fastest, in which direction should it crawl?

Question 5 - A student measured an angle θ = 41 ± 1^o. Convert the value to radians. Calculate sin(θ). Evaluate the uncertainty in the measured value of the sin θ. Note that the uncertainty in θ, δθ is not equal to the uncertainty in sin θ, δsin θ. One simple way of determining the uncertainty in sin θ is by δsin θ = (sin θ_max - sin θmin)/2, where θ_max = θ + δθ and θ_min = θ - δθ. Remember, that any uncertainty calculation is just an estimate, so don't report more than two significant digits. Please show work and formulas.