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using Greens theorem in the plane evaluate ∮(3x+4y)dx+(2x-3y)dy where C is the circle x²+y²=4 traversed in the counterclockwise sense
If fie=2x+2, evaluate volume integral where R is the region of the cube bounded by the plane x=0 ,x=1, y=0, y=1 ,z=0, z=1
Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.
Find an approximate value of the double integral below where 𝑅 is the rectangular region having
vertices (−1, 1) and (2, 3). Take a partition of 𝑅 formed by the lines 𝑥 = 0, 𝑥 = 1, and 𝑦 = 2, and take (𝑢𝑖
, 𝑣𝑖) at the
center of the 𝑖th sub region.
∬(3𝑦 − 2𝑥
2)𝑑𝐴
𝑅
what is the radius of the circle increases at the rate of 0.01 inch per second, find the rate of change of the area when the radius is 3 inches long
Evaluate I = Z C x^ 2 ydx + (x-2y)dy over the part of parabola y=x^2 from (0,0) to (1,1)
compute the directional derivative of r?r? at the point (1,-2,1) in the direction of normal to the surface xy^2z=3x+z^2,where =2x^3y^2z^4
[DE] Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).
- {x2, x+1, x-3} ans, W=8, linearly independent
- {3e2x, e2x} ans, W=0, linearly dependent
- {x2, x3, x4} ans, W=2x^6, linearly independent
Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3
29. Let f be the function given by ( ) 2 x f x xe− = . From the values of x given below, find a value of x so that the slope of the line tangent to the graph of f at ( xfx , ( )) is equal to 0.2?
