Reference no: EM131058999
1. Find the equation of the tangent plane at the given point.
z = ln(x3 + 1) + y2 at the point (0, 8, 64).
2. Find the equation of the tangent plane at the given point.
z = 3ey + x + x4+ 5 at the given point (2, 0, 26)
3. Find the local linearization of the function f(x, y) = x3y at the point (5, 1).
4. For the differentiable function h(x, y), we are told that h(700, 100) = 400 and hx(700, 100) = 11 and hy(700, 100) = 08. Estimate h(706, 98).
5. (a) Find the equation of the plane tangent to the graph of f(x, y) = x11exy at (1, 0).
(b) Find the linear approximation of f(x, y) for (x, y) near (1, 0).
(c) Find the differential of f at the point (1, 0).
6. (a) Find the differential of g(u, v) = u2 + uv
(b) Use your answer to part (a) to estimate the change in g as you move from (4, 5) to (4.1, 5.2).
7. A right circular cylinder has a radius of 50 cm and a height of 110 cm. Use differentials to estimates the change in volume of the cylinder if its height and radius are both increased by 2 cm.
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: A right circular cylinder has a radius of 50 cm and a height of 110 cm. Use differentials to estimates the change in volume of the cylinder if its height and radius are both increased by 2 cm
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