(a) ff f(x, y) da R dA = ["f" } ³² f(x, y) dy dx

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Q: Given f(x, y) = -6x¹ + 6x³y - 2y³, find fz(x, y) = fy(x, y) = faz(x, y) = fry(x, y) =

A: Since you have posted multiple questions, as per guidelines, we are supposed to answer only three…

Q: Find the solution of the differential equation r" (t) = (e6-6, ²-1, 1) with the initial conditions…

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Q: РОФ 0 TO 0, п,

A: The spherical coordinates are given as ,Transform the spherical coordinates to rectangular…

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A: given

Q: Letf(x)=1-x. If the region humed by the curve and x and y exis is revolved about the axis X=1, Find.…

A: f(x) = 1 – xIf the region bounded by the curve and x and y axis is revolved about the axis x=1Find…

Q: Evaluate the limit for r(t) = (t-², sin(t), -5). -2 lim h→0 r(t + h) - r(t) h - (f(t), g(t), h(t))

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Q: 4. How do we get the graph of y=-In (x+2) from graph of y= In (x)?

A: The function is

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Q: Find the equation of the sphere passing through P(-2, 7, 6) and Q(8, -5, 7) with its center at the…

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Q: Evaluate the following integral by first converting to polar coordinates. Z 2 −2 Z 2 − √ 4−x2 cos(x…

A: x is varying from -2 to 2y is varying from - to 2The region is a circle which lies only in first two…

Q: Problem.4. Sketch a graph for f(x) so that the following properties are true: lim f(x) = 5 Property…

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Q: 9. Determine the solution to the following system: x-y +z = 10 2x + 3y - 2z = -21 2 1 1 1 2x + 5y +…

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Q: 2. m, ne N. (a) You are given that limx→ (x log x) lim [xm (log x)"] X→0 Use L'Hôpital's rule to…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 4 Compute f'(3) for the function f(x)=. x² +5 (using the definition)

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Q: ( M for differentiation, which of the following c. sin (-1) u-cos^(-1) u D. -tan (-1) u+cot^(-1) u…

A: Three term given find the to reference the rule of differentiation which expression is constant.

Q: (a) Consider the first order separable differential equation (2x+3)(y² - 4) dy dx - (i) Find the…

A: Given that, the differential equation is                      (i)

Q: Compute the derivative (r₁ (1) r₂(t)) if r₁ (1) = (1³,1³,16) r₂(t) = (e²¹, est, e71) (Use symbolic…

A: two corruptions are found in your answer are;1) express answers by using a 'comma' instead '+'…

Q: c) Find the equations of the tangent lines to the curve In(x² + xy) = 1+z²y at the points where it…

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Q: The population Pof a city is modeled by the exponential growth model, P(t) = 12,500e0.03t, where t…

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Q: In The length of time, t (in days), for 100 flowers of a particular variety to grow to a population,…

A: Solution in details given below in step 2.

Q: Based on data from 298 of 351 cities and towns in Massachusetts, the average single-family property…

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Q: 9. True or false: lim x = -1 X+1 1= x² 11 -IN 2

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Q: Evaluate: fx²e4x dx

A: Given data

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Q: Question 2 Apply the linearity to find the transformation a) f(1)-1+r b)/(0)-2- <)(1)-2-…

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Q: How would I solve when it asks this? Using the same equation as previous

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Q: We want to use the Alternating Series Test to determine if the series: k3 √k8 +2 Σ(-1)*+2 k=4…

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Q: Find the domain of the function. (Enter your answer using interval notation.) 1 x2 + 5x f(x) = - 14

A: Given f(x)=1/(x^2+5x-14) To calculate domain for this function

Q: 6. Local farmers nurture a plant which grows at the rate of = 1.8t+4 (where t is the time in years…

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Q: (c) Hence compute x6(log x)5 dx.

A: From part a we have results

Q: Solve the following equation for x. 6* = 216

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Q: (2) Solve for y in terms of x In (2y+1) + 3x = 1n (4) -1 given

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Q: Test the series below for convergence using the Root Test. 2n +5 5n+1 The limit of the root test…

A: The given series .We have to check the convergence of the series using the root test.

Q: 6. Evaluate limx Sin (3x) 4x

A: let

Q: Q2 dy Find the using implicity differentiation. dx 1) a cos(xy) + e*+y

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Q: (13) Sup (14) The coefficient of x3 in the Maclaurin series expansion of e2x is: A) - B) C)- D) is…

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Q: 1. Perform the indicated operation. X (1-2x)3 dx

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Q: Find the location at t = 3 of a particle whose path satisfies = (181 +7+12+21-4) 2t r(0) = (8,7)…

A: To evaluate r(t) at t =3.

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Q: Suppose an experimental population of amoeba increases according to the law of exponential growth.…

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Q: Find the general solution of x²y" - xy' + y = x ln (x)

A: