10) If f(z) is analytic at all points in the region bounded by the simple closed curves C₁ and C₂ then a) f(z)dz=f(z)dz b) f(z)dzz f(z)dz c) f(z)dz=f(z)dz d) NOTA
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- Calculate the are bounded by the curves: A. y = x2 and x2 = y B. y = ln x and x - y - 4 = 0 C. y = e2x and x - 2y + 5 = 0find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of f(x,y,z)=x-y-z.Determine a region of the xy-plane for which the given differentail equation would have a unique solution whos graph passes through point (x,y) in the region. (y-x)y' = y +x
- (The Second Derivative Test) Let f : [a, b] → R be differentiable on (a, b). Suppose c ∈ (a, b) is such that f '(c) = 0, and f ''(c) exists. (a) If f ''(c) > 0, prove that f has a local minimum at c. (b) If f ''(c) < 0, prove that f has a local maximum at c. (c) Show, using two specific examples, that no conclusion can be made if f ''(c) = 0.An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called _____ is a constant.How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help in advance. :)
- If z = f (x, y) is a function that admits second continuous partial derivatives suchthat image 1 A critical point of f that generates a maximum point is: image 2Compute the line integral∫C [2x3y2 dx + x4y dy]where C is the path that travels first from (1, 0) to (0, 1) along the partof the circle x2 + y2 = 1 that lies in the first quadrant and then from(0, 1) to (−1, 0) along the line segment that connects the two points.Let f(x, y) = cos(x)cos(y). Find all critical points of f which lie in the square {(x, y) ∈ R2 : −1 < x < 4 and − 1 < y < 4} and classify each as a local maximum, local minimum, or saddle point.