If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

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

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Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

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Q: For which values of t is the curve x = ln t, y = et concave up?

A: given curve x=lnt  , y=et

Q: The line with equation 2x + 4y +7 =0 (a) Cuts the x-axis at the value x (a) Cuts the y-axis at the…

A: Given that: 2x+4y+7=0

Q: (a) z = x² + y² – 4x in P(1,2) (b) z = yln(x +y) in P(-3,4) %3D

A: a) Compute the gradient of z=x2+y2-4x in P1,2 as follows: It is known that the gradient is…

Q: 21 Given the curve x + y? + py –q =0 where p and q are constants. dy a. Find dx b. If the gradient…

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Q: Find the gradient of the function at the given point.

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Q: For Parts (a) (b), find the gradient at the given point. (a) f(p, q) — 6р? + 3q? + 2рq at (1, —2)…

A: Answer is mentioned below

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 to the equation xy f(x, y) 2. at the point (4,6,4), and use it to…

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Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

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Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: 2 Find the gradient of a line which is perpendicular to each of the following lines: a y=-3x+ 11 +2y…

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Q: Q2: Discuss the fundamental theorem for gradients usingE = 5x2 î + 20 xy j+ 10 yz3 k and the…

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Q: Q3: Find gradient of the following function at given point 3) f(x, y, 2) = x² +y² – 2=² + = In(x).…

A: The gradient at the point (1,1,1) is, (3, 2, - 4)  The detailed solution is as follows below:

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Calculate the gradient of the following function fox, y) = (x – 2)^3 sin y, at (0,0]

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Q: Find the gradient of the following function. 3 f(x, у) %3 5x° - ху Vf(x, y) =

A: Gradient of f(x,y) is given by∇f(x , y) = i⇀ ( fx ) + j⇀( fy )

Q: Let f(xv) = 2x3 – 4xy + yt. Give detailed explanations for your answers to the %3D following. (a)…

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Q: Calculate the gradient of the tangent to the following curves at the given 1 y = 3x', x = 1 y = 2x –…

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

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Q: f(x, Y, z) =

A: We are asked to find the gradient of the function.

Q: For function f (x, y) x2+1 Evaluate the gradient at the point (1,2) 2.

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Q: 25 Find the gradient of f(x, y) : at (-2, 1). x² + y? NOTE: Enter the exact answer. grad f =|? i+ ?…

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Q: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

A: As per our guidelines we are supposed to answer only first three subparts of the question. Kindly…

Q: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: Consider the following. w = xyz, X = s + 5t, y = s - 5t, z = st? (a) Find dw/ds and aw/at by using…

A: Solve the following

Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 4, (3, 2) %3D Vf(3, 2) =

A: We will solve the problem.

Q: 1. Find the Gradient of the following F = x*e" - y': b. F, = 4x - 3y + 5=? а.

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Q: Solve for the gradient of the given function. f(x, y) = e¤ sin y + el cos x

A: Given,  f(x,y)=ex sin y+ey cos x

Q: Suppose z is implicitly given by the equation x³y-yz²+ -5 x In a neighborhood of the point P(1, 1),…

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Q: Which of the following functions has a gradient of 1 at x = 0 ? Select one alternative: y = √x y =…

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Q: Given that Vf(8, –2) = 8 i – 6 j, find the directional derivative of the function f at the point (8,…

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Q: Find the gradient of z = (7x + 4y)e. Assume the variables are restricted to the domain on which the…

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Q: Find the gradient Vf at the given point, and compute the directional derivative of the function in…

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Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Given that Vf(10, –12) = 11 i – 10j, find the directional derivative of the function f at the point…

A: Given:- Given that ∇f(10, −12) = 11 i — 10j To find:- The directional derivative of the function f…

Q: If f (x, y) = x² + 4y² , use the gradient vector Vf(3, 1) to find the tangent line to the level…

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Q: For what values of x will the curve of y = x(x² – 12) has zero gradient? %3D

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Q: Given that sin(any) + axy2 – a = 0, where a is a non-zero constant, find a formula for the gradient…

A: Given: To find the formula for the gradient of the tangent to this curve at a point P(X, Y) on the…

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: Find the gradient of f(r, h) = 2arh + ar² at (7,7). NOTE: Enter the exact answer. grad f =| ? i + ?j

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Q: hFind the gradient of the function at the given point. W = x tan(y + z), (19, 4, –1) Vw(19, 4, –1) =

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Q: Determine the gradient of following functions at the given points: (t) = (2t7 + P t-2)² + (6vt – 5)…

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Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2,1)

A: We find the gradient of the given function by using the definition of gradient. The gradient of a…

Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: You know that d/dt f(r(t)) = 69 at t=7 if r(t) = [t, t] and d/dt f(r(t)) = 21 at t=7 if r(t) = [t,…

A: Given that , ddtfrt=69 at t=7 if rt=t,t and ddtfrt=21 at t=7 if rt=t,14-t find the gradient of f at…

Q: Given curves 7(t) (5t, 3t, 5t 5) and ü(t) = (3t°, 2, 4t + 6t) find the derivative of the cross…

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