Let Ax,y) = 5x + 5xy – 6y. Give the coordinates of a point on the graph of f at the point (3,6). O A. No correct Answer О в (-81,3, 6) ос (3,6, -81) OD (5,5,3) O E (3,5,5)

Q: Let f(x,y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2,3)=-3 and f7(1,-2,3)=2. What is the…

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Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the…

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Q: Evaluate F dr where F(r, y, z) = (2.75yz cos(ryz), 2.75rz cos(ryz), 2.75xy cos(ryz)) and C is %3D 1…

A: Here we will find out the required value.

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: Find the derivative of f at point P in the direction of u. f(1, у, 2) — Зг? + 8y? - 42?, Р — (9, 2,…

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Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

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Q: Evaluate | F· dr where F(x, y, z) (4yz cos(xyz), 4xz cos(xyz), 4xy cos(xyz)) and C is the line C 1…

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Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

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Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Let f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2.3)=-3 and f-(1,-2,3)=2. What is the…

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Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: Let f(x, y, z) = 5x³ – y + z?. Find the maximum value M for the directional derivative at the point…

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Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Suppose that Vf(x, y, z) = 2xyze*i+ ze**j+ ye*´k. If f(0, 0, 0) = 5, find f(1, 1, 8). Hint: As a…

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Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: ask 4. Let F(z,y) = [2ry² + 1, 2r²y + y]. i) At the point (3,3) in which direction is the…

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Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

Q: Let f(x,y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2,3)=-3 and f-(1,-2,3)=2. What is the…

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Q: If W[y, , y2• Y3]=0, then {y1 , y2 , y3} must linearly dependent, where y1 , y2 , y3 are…

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Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

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Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: Find the Direcctional derivatve of the function foxxy,z)=tan(xjz) aut point (t,2,4) in the direction…

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Q: Let f (x,y)=x2+5xy−4y2. Then a standard equation for the tangent plane to the graph of f at the…

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Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

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Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at…

A: The given function is: f(x,y)=x2+y3Direction vector is:  v→=4, 3Given point:  P=(1, 2)

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Show that the curve In (2X-1) , n> i has no stationary point

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Q: Given a function (r, y, 2) = 3x2 + In (3y2+ 1) + e cos 2. i. Find the directional derivative of o at…

A: Here we will find out the required value.

Q: Let f(2, y) = In(' + 2 xy). Find the directional derivative of f at the point (1,1) in the direction…

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Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: Calculate Duf(– 1,4, 5) in the direction of i i- 2j – 2k for the function %3D f(x, y, z) = 2x2 – 2xy…

A: Basics of Vector.

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

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Q: 3.8 If H = (x – y)a, + (x² + zy)a, + 5yz a, evaluate f H dl along the contour of Figure 3.28.

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: Check whether z/z+3 is analytic or not by C-R equation?

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Q: Let f(x, y, z) = 5x – y + z?. Find the maximum value M for the directional derivative at the point…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.