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EBK CALCULUS EARLY TRANSCENDENTALS SING
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
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- Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin(t). Find af af and (write your answers as functions of the pair r and t). Ot Or af Or af ICHarrow_forwardFind the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 7xy2, (3, −5) maximum rate of change direction vectorarrow_forwardSolvearrow_forward
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- 2 Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction of the vector i + j. √5 √5 (Use symbolic notation and fractions where needed.) directional derivative:arrow_forwardFind the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction of the vector 1 2 i+ (Use symbolic notation and fractions where needed.) directional derivative:arrow_forwarda) Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i+j+ 2k.arrow_forward
- Solve part (b) onlyarrow_forward2. Calculate the gradient vector Vf of the function f (x, y) = x² – x + y - x²y - 2y2 at the point (2,1) and sketch it on the attached contour plot (you can save the picture, open in photo editor and use drawing tools). Explain in one paragraph (about 200-300 words) the meaning of the gradient vector Vf(2,1), negative gradient vector -Vf(2,1).arrow_forwardI'm stuck on this one. I need help please & thank you!!arrow_forward
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