Consider the function R° → IR Draw f(x, y) = y2 + x(x - 1)2(x – 2) alignment curves. |

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

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Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(xy) + y² + 2y) (b) Use your…

A: Solution of given question is followed by:

Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: Integrate the function f (z) = (z – 8i)- from z = 0 to z = 4 + 4i along the line x = y.

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Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

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Q: Find the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x y f(x,y) = at (1,2) 1…

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Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

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

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Q: Find the linear approximation of the function below at the indicated point. f(x, y) = V 17 – x2 –…

A: Givenf(x,y)=17-x2-4y2  Point (2,1)

Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1…

A: Linear approximation to the function f(x ,y) at (a, b) :       L(x ,y) = f(a ,b) +(x-a) f x (a, b) +…

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: Integrate f(x,y) =x -y over the curve C: x² + y = 16 in the first quadrant from (0,4) to (V8,18 - y)…

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Q: Exercise III. Find the length of the curve a) x = t³ y = t2 0<t< 4 b) x = cost y = sint 0 <t< 2n c)…

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Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: Integrate f(x,y)=x²-7y over the curve C: x² + y² = 64 in the first quadrant from (0,8) to (√32.√32)…

A: Draw the given equation of the curve x2+y2=64 and the given points. The given curve is between…

Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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Q: Match the function with its graph. (x, y) = 1+ x +y p Kx, V) = (x² – y²)* %3D f(x, v) = sin(Ix| +…

A: Answer is mentioned below

Q: Consider the function f(x, y) = xª + y4 – x² – y? – 2xy. Find its stationary points. Show that one…

A: Given :

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: 5. Let f(x, y) = xe" + cos(xy) and P: (2,0). %3D A. Find the directional derivative of f at P in the…

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(ry) + y² +2y) (b) Use your…

A: (a)According to question given :F→=y cos(xy), x cos(xy)+y2+2yWe have to calculate for f(x,y)As we…

Q: Integrate the function f (z) = (z - 8i)² from z = 0 to z = 4 + 4i along the line x = y.

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Q: dy Assuming - 9x³ - 2y - 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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