4-(12+13 p.) (a) Find the derivative of f(r, y, 2) = xe+ In(z2) at Po.0,) in the direction of 21 +j- 2k. (b) Find the equations for the tangent plane and the normal line at Po(1,-1,3) on the surface r + 2ry - y? + 2 = 7.

Q: The directional derivative of f(z, y,2) = r'y- v': at the point (3,2,1), in the direction of the…

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Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

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Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

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Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

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Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v…

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Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: Find the direction derivative of f(x, y, z) = x²y - zx -yx point (1,-1,1) in the direction 3i+4k %3D…

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Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: Let f(r, y) = - (5x² + 4xy+ y²). Then an implicit equation for the tangent plane to the graph of f…

A: Given function is, fx,y=−5x2+4xy+y2 To find the implicit equation of tangent plane to the graph of f…

Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

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Q: Find the equation of tangent and normal lines to the curve xs sin(2y) = y cos(2x) at the ㅠ ㅠ point…

A: Solution of this question is

Q: 5. Find the equation of the tangent plane of sin(xyz) = x + 2 y + 3z at the point (2, -1, 0).

A: We have given the surface X,Y,Z at the point (2,-1,0). We have to find the equation of the tangent…

Q: Find the derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

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Q: 3. Determine the equation of the tangent plane and normal line to 2xz + y²z³ = x + 5 at (1,0,3)

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Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

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Q: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.

A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)

Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

A: Let's find.

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: 2xy - y² + x = 2 at the point (1,2). - Find the equation of the tangent line to ² +2

A: By using equation of tangent line formula, we find the required tangent line.

Q: Find the equation for the tangent line to the curve f(x)=cos(x)-2sin(x) at the point (0,1). O y=-x+1…

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Q: Let (x, y) = 3y² - 2y – 3x² + 6xy. a. Find the equation of the tangent plane at the point (1, -1).…

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Q: 0Y Find the direction derivative of fcxy)=xy at the paint (2,1), by the dirction of v- i-j

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Q: The directional derivative of f=8x²y-2xy²+3z at point P(1,1,2) in the direction 2âg+2ây-âz is

A: First we find the gradient of the function f and then unit vector.

Q: 9. Approximate (4.1)² using a linear (tangent) approximation off of the point (4, 16) on the curve y…

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Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

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Q: Determine the equation of the tangent to the curve y = sinx +cos(2x) at the point 6. 1) Py-1= -(--3)…

A: First I have written the formula of tangent line to the curve at a point , just use that formula for…

Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

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Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function f(x, y, z)=(x3-xy2-z).........(1) We have to find the derivative of the function…

Q: 9. Find the directional derivative of f(x, y) = 3x² – y² + 5xy at (2,–1) in the direction of -3i –…

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Q: 3 Find the equation of the tangent line to the curve x*y – xy = –2 at the point (-1, –1

A: Given: x4y-xy3=-2 and the points are (-1,-1)

Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: The gradient of the tangent to the curve = 4x + y at the point (0, 1) is D - 2

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Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: Find all​ x-coordinates of points​ (x,y) on the curve y=(x−2)4(x−5)-3 where the tangent line is…

A: Given,          y=x-24x-5-3 where the tangent line is horizontal.

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.