Find the Zero and its oodex for the function flz)=1- Ti+Z+

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

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Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: Find the linear approximation of the function f (x, y) = 2x – y+x?y - near the point (2,0). O 2x +…

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Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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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: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

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: Find the number of zeros of f(z) = z3 + z* + 2z2 + 1 in the first quadrant. %3D

A: Given that,     fz=z13+z4+2z2+1

Q: Find a point zo where the function f (z) = (z – 12 – 12i) (z – 12 – 12i) is differentiable. What is…

A: Given f(z) = (z-12-12i)(z -12 -12i)¯

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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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: Find a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

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Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

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Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

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Q: Determine the linear approximation of f(x) = at z = 1. O a. y= 9x +8 O b. y=- 9 x-8 O c.y = 9x - 8 O…

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

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

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Q: Find PSD of Y (i) interms of X (1). Assume O is independent of X (f).

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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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: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

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Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: Find the linear approximation of the function f(x)= cuberoot(1+x) centered at 0. Use this to…

A: For the solution follow the next step.

Q: Find the two positive x and y such that x+y=60 and xy2 is maximum

A: We have to find x and y in the given question.

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: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Find the isogonal trajectories of x²=2Cy, theta=45°

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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: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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