Find the image of the given point under the given translation. P(6, 10) T(x, y) = (x – 7, y + 8) P' = ([?], [ ]) %D Enter the number that belongs in the green box.

Q: Find the equations of the normal line to the surface z = 8x°y" at the point (– 2, – 1,64). y = z = -…

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Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: How can the position and the velocity of K be described at the moment that L passes through the…

A: The position of the point on the curve can be defined by the x-axis and y-axis coordinates of the…

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 3.…

A: Given ∫Cz3-4x+2y dswhere C is the line segment from 2,4,-1 to 1,-1,0

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (3y) at the points (0,0) and0,

A: Answer is given below

Q: 2. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

A: y=ax3+bx2+cx+d-1Critical points 1,0-2,27We know that at critical point dydx=0 or does not exist…

Q: 1. Find the length of the curve y = 3 xi - () x , from x = 1 to x = 4.

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Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: 1) Evaluate S,(x – y)dx + (y – z)dy + xdz where C is the curve from (1. –2, 3) to (–4, 5, 2) if a) C…

A: Given integral: ∫Cx-ydx+y-zdy+xdz Here, C is the curve from 1,-2,3 to -4,5,2 a) The parametric…

Q: find an equation for the level surface of the functionthrough the given point. ƒ(x, y, z) = √(x - y)…

A: given,  ƒ(x, y, z) = √(x - y) - ln z, (3, -1, 1)

Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy + 2 at Po(5,2). Then find an upper…

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Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy +8 at Po(5,5). Then find an upper…

A: We have to find the linearization L(x, y) of the function f(x, y)  and then find an upper bound for…

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: The length of the curve y = from x = 0 to x 6 is

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Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: 3) Evaluate elz+y)/(z-y) dA where Ris the quadrilateral with vertices (0,1), (0,-2), (1,0), and…

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Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

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Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: A particle is moving with the given data a(t)= 3e^2t -2 cost, s(0)=0 and v(0)=0, find the position…

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Q: 2. Find the absolute maximum and minimum values of f(x, y) = 4x+6y-(r²+y?) on the rectangular region…

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Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: 13. y = x², y = 0, x= 1; about the y-axis

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Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 4.…

A: Given ∫Cy2-3z+2 dsC is the line segment from 1,0,4 to 2,-1,1

Q: 1. Find the exact length of the curve. (a) y² = 4(x+ 4)°, 00 (b) y = In z, 1<I<2

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Q: The line tangent to a curve at a point (x1, y1) is y = 2x – 2. The normal to that curve at the same…

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Q: (A) Evaluate z dz along from z= 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 4. 3x? ey dx + e dy C C: boundary of the region lying between the squares with vertices (1, 1), (-1,…

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Q: Find the values of dz/ôx and az/ðy at the points 31. z - xy + yz + y -2 = 0, (1, 1, 1)

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Q: Mike found the orthogonal line to the curve f ( x) = – 3sin( ax) + 1 at x = -1. In which step did he…

A: If a curve is f(x), then the orthogonal line to the curve at point (a,b) is called a normal line.…

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

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Q: 5. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

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Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

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Q: 3. Find the orthogonal trajectory of the given family of curve x2 + y² = C1

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Q: B. An unevenly heated plate has temperature T(x, y) at point (r, y). If T(2, 1) = 135°, T,(2, 1) =…

A: Given that T is the temperature and T(2,1) = 135, Tx(2,1) = 16 and Ty(2,1) = -15 The linear…

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &amp;…

Q: 6x Find the linearization L(x,y) of the function f(x,y) = e cos (y) at the points (0,0) and

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