Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to find at (r, 0) =(√2, 7). de

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A: Given the query is to find the point of diminishing returns.

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A: We have to find integral solution

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A: Given : apply chain rule    find limit of about separately

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A: There is more than 1 question, as per the Q&A guidelines I am answering the 1st question. If you…

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A: Follow the procedure given below.

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A: Area under the curve over the given interval:3, 6Area: ∫abf(x) dxA =∫36 (8ex-x) dx   =8ex -x2236…

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Q: For what values of x does the series converge conditionally? 5x Σ n! n=1 1 O A. x= -7 5 OB. X=0 1…

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Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: dr

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Q: Determine whether (-2, 3, -8) can be written as a linear combination of u(1, 1, 1) and v(1, 2, 5).

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Q: 8. Determine if 2n-1 [5 -1 is cont 7n n=1

A: Given

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A: We can answer the question as below.

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Q: Which of the following Cartesian equations is equivalent to the polar equation T= 4 cos 0? Select…

A: We can convert from polar to cartesian equation as below.

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A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) &gt; 0?   b. On what…

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A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

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A: Critical points are the points of a function where the derivative does not exist. local maxima: the…

Q: Problem 3. Solve [2*+2³ = 10 4* +4" = 68

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A: To solve the given differential equation.

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A: As per our guidelines, we can help you in solving only first problem, rest of the problems you have…

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Q: (4n². En=1 2 - 2n + 6, - limit comparison test -1 (8,² + n – 8) 7

A: The given series,      ∑n=1∞4n2-2n+68n7+n-8

Q: If A =27+7-, B =-T+27-4k, and A +B +C =27+7+ 2k, what is C? 7.

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Q: A teacher has prepared 20 mathematic and 30 geometric and 25 physics questions for a test he can…

A: This question can be solved using the concept of combination.

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: 4. (- FIND the center of mass of the lamina of density p if the lamina is shaped like the region…

A: A detailed solution is given below.

Q: The particular solution of the following equation by using the D Operator y" + 2y' + 3y = -2x + 3

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Q: B) Find the number of bacteria after 5.5 hours.

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Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

Q: Find the center of x 2 + y 2 - 10x - 8y + 1 = 0. (5, 4) (-5, -4) (-10, -8)

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Q: f(x)=x√ 36 = x² ntercepts (x, y) = (x, y) = (x, y) = elative minimum (x, y) = elative maximum (x, y)…

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Q: x² + 4xy + y² = 13, (2, 1)

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Q: In order to evaluate Vr2 – 10x + 29 dx, the correct substitution is Ox=-5+2 tan(t) Ox=2+5tan(t) Oa =…

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Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

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Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: dy 1. Find general solution for =x²y° +2y +x° +2. dx

A: Dear learner,  As per our guidelines we can provide the solution for first one only. Kindly post…

Q: -4 -3 Find the eigenvalues of matrix 6. 5 A. 1 & 2 B. -1 & 2 C. 1 & - 2 D. -1 & -2 E. None

A: Let's find.