If the equation F(x.y,z) = 0 determines z as a differentiable function of x and y, then, at the points where F, # 0, the following equations are true. Fx Fy dz and dy dz = - F. Use these equations to find the values of dz I dx and dz / dy at the given point. 3z° - xy + 5yz + 2y° - 60 = 0, (4,3, 1) |(Type an integer or a simplified fraction.) dx |(4,3,1)

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Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

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A: Length of the given curve will be

Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

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A: The objective of the question is determine the length of the curve.

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A: Use the chain rule of derivative and substitute the given value then simplify to get the send and…

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A: Explanation and solutions is given below....

Q: II. Find the acute angle between the given curves. 1. y'=2x^4x+4y'+5 y=0 2. x'y+4a y=8a°nx²=4 ay 3.…

A: As per bartleby guidelines we only give first question answers.

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A: According to our guidelines, we can answer only the first question, the rest can be reposted.

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Q: Which one of the following equations describes the tangent plane to the curve, f(x, y) = x² + y² +…

A: Explanation of the answer is as follows

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A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

Q: I. Find the acute angle between the given curves. 2. x'y+4a° y=8anx²=4 ay 3. x*y+4y=8Ax²y=4

A: We have to find the acute angle between the given curves: x2y+4y=8 and x2y=4

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Q: If the equation of the tangent plane to x2+y2-11z2=0 at (1,1, /2/11) is x+ay+Bz+y=0, then a+B+y=D

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A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

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A: Option A is correct answer, Detailed explanation is given below.

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Q: h) $ dz =. 1) where C is a positive contour outside of a point z=i= (0,

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A: Topic = Derivative

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Q: II. Find the acute angle between the given curves. 2. x'y+4a° y=8anx²=4 ay 3. x'y+4 y=8Ax*y=4

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Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

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