Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1 ху L(x.y) =D

Q: The initial heat distribution over a steel plate is given by the function: u(x, y) = 80y²e-0.3y Plot…

A: The graph a three dimensional surface is represented by the equation, z=f(x,y). If the graph of…

Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Find a gradient of the equation: F(x,y) = v2x + :- y sin a + 4 VF =?

A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

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Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

Q: Find the linear approximation to R(t) = Vt: %3D at t=32. Use the linear approximation to approximate…

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Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: (i) Find the equation for the tangent plane to 2 2 z=f(x, y) = 2x +3 y at the point (2, 2, 20). (ii)…

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Q: Use the technique of variation of parameters to find a particular solution to the DE y" – 2y + y =…

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Q: Find the directional derivative of the function f(x, Y, z) = 3e" sin(xy) in the direction of v =…

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Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

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Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and…

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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: Find ow/@s and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x S+ t, y =…

A: Given that function w=sin2x+3yx=s+t , y=s-tvalue s=0 ,t=π2To find :∂w∂s,∂w∂tSolution…

Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

Q: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

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Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

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Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

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: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

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Q: 1. For the function f(x, y) = In root (2 + xy), find the equation of the tangent plane at the point…

A: Note: As per the guidelines we are supposed to answer only one question because this is not a…

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: ,use the linearity of L   determine L[f]. Q. f(t)=sinh bt, where b is constant.

A: Given, f(t)=sinh(bt), where b is constant To determine L[f].

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: 2. For the function f(x,y) = 3x + 4y – xy a) Vf(1,2) = b) Find the directional derivative of f at…

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Q: 1. Find the directional derivative of f(x,y) = y²e²" at (0, 1) in the direction of v =.

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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: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: A suitable substitution to transform the D.E. t dy – y dt = tydt into linear equation will be :

A: Substitution to convert given differential equation into linear

Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,

Q: Find the values of constants a,b.c such that the maximum value of the directional derivative of f…

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

A: definite integrate calculus