(i) g(x, y, z) = In(3.x²yz); . %3D

Q: Consider the following. g(x) = (5x – x³) h(x) = (3x + 4) f(x) = (5x – x³)(3x + 4) Find g'(x) and…

A: gx=5x-x3hx=3x+4fx=5x-x33x+4

Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

Q: J In(x² + 1)dx

A:

Q: c) Determine a pattern for the value of the even, (2k)", derivative of f(x) at x 37T th d) Determine…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y = fx) 8.…

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Q: (c) f(x, y) = V3x + y?, x = 2, y = 0, dx = 0.01, dy = 0.01. %3D %3D 1 f. 2/3x + y? 3 (i) 3x+y? (ii)…

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

A: Find your answer below

Q: Solve for the function f(t) of the Laplace transform. S-1 F(s) (s+1)(s²+4)

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Q: dz (a) Find of the following functions: dx zx2+1cos y? = sin(y? + 22z)

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Q: Let f(x) = r³ – 3.r² + 4. Using the Mean Value Theorem, determine the value of c € (0,3) such that…

A: Given    f(x) = x3-3x2+41. Continuity:     we know that, every polynomial function is continous in…

Q: Use the ratio test to discuss the Con vergence or divergence of the seríes which s the Sum from n1to…

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Q: Convert the point (x, y) from Rectangular to polar coordinates (r, 0). 3. (–1, v3)

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Q: dz of the following functions: Find dx 8 zx*+cos y? = sin(y °+ 22z)

A: Find your answer below

Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

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Q: Find the limit of the sequence: 4n? + 2n + 3 An 4n2 + 6n + 2

A: limn→∞ 4n2+2n+34n2+6n+2=limn→∞ 4+2n+3n24+6n+2n2=limn→∞ 4+2n+3n2limn→∞ 4+6n+2n2=44=1

Q: 4. Use the given graph of a functionf to answer the following questions. y= f(x) a. State all the…

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Q: x2 – 25 dx 7) S-

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Q: Jse the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? O…

A: We have to find the vertex

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) V…

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Q: Consider the following. u = 3i - j- k, v = -i + 5j + 7k %3D (a) Find the projection of u onto v. (b)…

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Q: Solve the following system of differential equations. dx —х — у, || dt dy Зх — у dt

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Q: d d Calculate ri(t)·r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

A: In the given problem first we differentiate the product directly & then we use the formula for…

Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: What is the area under the graph of y = 2- x on the interval -2, 1]? X 543-2 44 1 2 4 5 O 6 13 15…

A: Find area under the graph

Q: Evaluate the indefinite integral. dx 2 – 7x

A: Explanation of the answer is as follows

Q: п+1 Given that 0.47199 determine the value of ) n +1 n3 n=3 n3 n=5

A: Given: ∑n=3∞ n+1n3 =0.47199 To evaluate: ∑n=5∞ n+1n3

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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Q: 1. A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Consider the following. u = (6, -1, 0) v = (-6, 5, 0) Find u x v. Determine if u x v is orthogonal…

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Q: 2x) dx Find an approximation to the integral using a Riemann sum with right endpoints and n = 8.

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Q: A high-walled arena has a radius of 20 meters. Point O being the center, point A is along the…

A: Given that radius = 20 m. So, OA = OC = 20 m. Given OB = 10 m. So, BC=202+102=500=105 m.   Let, D =…

Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: A detailed solution is given below

Q: 1. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: nsider the Integral I when answering the following questions. g(x) dx

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Q: The geometric series 4 5-2+ 5 16 + 25 8 32 125 625 is convergent. true false

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Q: 3. The value of a certain baseballcard (in dollars) tyears after 2015 varies according to the…

A: Given function describes value of card t years after 2015

Q: Sketch the region of integration. (Select the correct graph.) "In 3 dy dx In y y y

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Q: Question A vertical cylinder is leaking water at a rate of 8 m³/sec. If the cylinder has a height of…

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Q: Find the volume of the solid bounded by the graphs of the given equations.   z = xy,    z = 0,…

A: Given problem:- Find the volume of the solid bounded by the graphs of the given equations.   z = xy,…

Q: Find the curvature K of the curve. r(t) = 9 cos(nt)i + sin(at)j K =

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Q: Q1. Choose the correct option: a) Let f(x) = |x]. Then at x = 0, the function f(x) is: %3D (A)…

A: This is a problem of limit and continuity parts. Please find the solution below.

Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both…

A: Given and Basic information:R=Rn, Revenue earned by selling 'n' tiresdollarsC=Cn, total cost of…

Q: Solve the following differential equation using variation of parameter. 4y" – y = xe"/2; y(0) = 1,…

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Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: 3. y" +4y = 0; yıi =cos 2x, y2 = sin 2x; y(0) = 3, y'(0) =8 4. y" + 25y = 0; yı = cos 5x, y2 = sin…

A: Note : "Since you have posted multiple questions, we will solve first question for you. To get…

Q: 1. sin²(esin*r) + cos-(2t³ – 5)

A:

Q: e2x :dx /1– ex

A: Given:        ∫e2x1-exdx  substitute u=1-ex→dudx=-ex→dx=-exdu  use e2x=1-u2      =∫u-1udu Expand:…