Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming that x, y, and z are nonnegative. Maximize f(x, y, z) = xyz Constraints: x + y + z = 32, x - y + z = 28 f(

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A: Solution: y=(x+5)^x dydx=ddx((x+5)x)

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Q: 4x2 + 21x + 54 x2 + 6x + 13

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A: Given that    sin(2x) and ln(1+x) To find 5th degree Taylor polynomial centered at x=0

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A: Given

Q: Evaluate (S (x + 2y)dy) dx. О а. 5/8 ОБ. 8/5 Ос. 3/16 O d. 16/3

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Q: Find an angle 0 with 0° <0< 360° that has the same: Sine function value as 250° 0 = degrees Cosine…

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Q: Suppose the temperature in degrees Celsius over a 10-hour period is given by T(t) = - t + 6t + 36.…

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Q: d(x,y) a. Solve the system u= 4x +3y, v=x+3y for x and y in terms of u and v. Then find the value of…

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Q: finite difference du n. = 0 en 0 0; dx² - u(0, t) = u(2, t) = 0, 0 < t; %3D u(r, 0) = sin x, 0<x <…

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Q: Find the volume of the region bounded above by the surfacez=9- y2 and below by the rectangle R:…

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Q: State the type of the quadratic surface: ()' - (5)' + (¿)° = 1 2 1. Ellipsoid 2. Hyperboloid of one…

A: Here we need to find the type of quadratic surface and it's trace obtained by the plane z=1

Q: 4x3/2-1 (a) f(x) = (b) g(x) = 3e" +sec? a h(x) = 8 sin x (c) 4 1+x? (d) f(1) = 5 cos x V1-a2

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Q: Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the…

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Q: %3D 3. For y = f(x) = 6x, x = 4, d and Ax 0.08 find a) Ay for the given x and Ax values, b) dy…

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Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

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Q: Find f. f"(e) = sin(e) + cos(e), f(0) = 5, f(0) = 4

A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…

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A: Here we have to solve the given integration by using integration by parts.

Q: if t ß (-2t + 1 h(t) = {t² 2+1

A: Topic:- limit and continuity

Q: Problem 3 If the nth partial sum of a series E1 an is п— 1 Sn n+1 find an and E=1an.

A: The given data is: Sn=n-1n+1  To find the value of an and ∑n=1∞an.

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Q: 3) Chain rule: y = (3x2 - 3x- 2)2 1/2

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Q: n y = -5e0.

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Q: 13x2 — 8х Find the horizontal asymptotes of f(x) = 14x2 + 5 (Use symbolic notation and fractions…

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Q: 4x2 + 21x + 54 -dx x² + 6x + 13

A: Given,            ∫4x2+21x+54x2+6x+13dx

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: The given function is: f(x,y,z)=xy+yz+xz Now, ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z…