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Calculus
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17 Nov 2019
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Find the gradient field F of the function f. 1) f(x, y, z) = x^4 x^8 + x^8/z^3 Evaluate the line integral of f(x, y) along the curve C. 2) f(x, y) = x^5/squareroot 1 + 4y, C: y = x^2, 0 lessthanorequalto x lessthanorequalto 3
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Suppose that a function f(x, y, z) is differentiated the point (0, -1, -2) and L(x, y, z) = x + 2y is the local linear approximation to f Find f(0, -1, -2), fx(0, -1, -2) fy(0, -1, -2) fz(0, -1, -2). A function f is given along with a local linear approximation L to f at a point P. Use the information given by determine point P. f(x, y) = x2 + y2; L(x, y) = 2y - 2x - 2 f(x, y) = x2y; L(x, y) = 4y - 4x + 8 f(x, y, z) = xy + z2; L(x, y, z) = y + 2x - 1 f(x, y, z) = xyz; L(x, y, z) = x - y - z - 2 The length and width of a rectangle are measured with of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.
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Suppose that a function f(x, y, z) is differentiated the point (0, -1, -2) and L(x, y, z) = x + 2y is the local linear approximation to f Find f(0, -1, -2), fx(0, -1, -2) fy(0, -1, -2) fz(0, -1, -2). A function f is given along with a local linear approximation L to f at a point P. Use the information given by determine point P. f(x, y) = x2 + y2; L(x, y) = 2y - 2x - 2 f(x, y) = x2y; L(x, y) = 4y - 4x + 8 f(x, y, z) = xy + z2; L(x, y, z) = y + 2x - 1 f(x, y, z) = xyz; L(x, y, z) = x - y - z - 2 The length and width of a rectangle are measured with of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.
aquamarinelouse815
Vector field F = M(x, y)i + N(x, y)j or F = M{x, y, z)i + N(x, y, z)j + P(x, y, z)k Position vector = xi + yj or = xi + yj + z k Distance function or Show that F = grad(xy)/||grad(xy)|| is a gradient of some function f(x, y) and then find the potential function f(x, y). Let F( ) = k/rn , where n is appositive integer, k is a constant, and = xi +yj +zk Show F( ) is a gradient vector field. Find the potential function f(x, y, z) such that f = F, if n = 2 ; n 2.
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