By about how much will ƒ(x, y, z) = ln(sqrt(x2 + y2 + z2) ) change if the point P(x, y, z) moves from P0(3, 4, 12) a distance of ds = 0.1 unit in the direction of 3i + 6j - 2k?

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Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

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A: To find the level curves, equate the function fx,y with a constant C.

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A: xy2=4 Differentiating with respect to x, we get…

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A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: 7. Find the area of the surfaces generated by revolving the curve r = 2e®² for 0<0s- about x- axis.

A: The solution are next step..

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A: Clearly from the above statement as second derivative is negative so the actual value is less than…

Q: Find the area of the segment cut off from the curve y = sin x, 0≤x≤ n by the line y = 1/√2. H4 34 y…

A: Let's find area of segment.

Q: How many points are there on the surface 2 dx+y such that the tangent plane to the surface is…

A: We have given the a=6,b=9,c=9 d=max(a,b,c)=max(6,9,9)=9 The given surface is f(x,y,z)=9x2+y2-z We…

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A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: Find the approximate roots of y = r - a +x – 3 between r = 2 and z = 2.5 by using either the…

A: Bisection method: Let f(x)=0 be equation, to find the roots of equation in interval a,b. Let us…

Q: The tangent line to a point on the curve r(t) = (3t2 + 2t+ 3)i + (t² + 2t + 4)j+ (2t2 +t+ 2)k…

A: Differentiate:

Q: The tangent line to a point on the curve r(t) = (3t² + 2t + 3)i + (t² + 2t + 4)j+(2t² +t+ 2)k…

A: Differentiate:

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

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Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

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Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

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A: By using differentiation mathematics detailed solution given below

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

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A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

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