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Q: Given the vector function F(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

A: Please refer to the image below

Q: Find the limit, if it exists, or show that the limit does not exist (a) lim (v) (0,0) 4+4y² U=D 15m…

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Q: If a rock is thrown upward on the moon with a velocity of 15 m/s, its height (in meters) after t…

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Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: 6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divĒ.

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Q: Find the general Solution of the complement OF the following differential equation y"-7y) -6y=013…

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Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: Evaluate the following integrals: a) b) ex² Jy/2 dx dy dy dz dx 2y

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dt 1³ +1²-2t

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Q: dx | | dt dy dt dz dt = 3x + 2y + 4z = 2x + 2z = 4x + 2y + 3z

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Q: Find all the values of x such that the given series would converge. ∑_(n=1)^infinity((−1)^n x^n…

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Q: Solve the following equations 63. y"+y = 3 sin 2x + xcos 2x

A: If   Qx=xF, where F is a function of x  then particular integral is PI=1PDxF=x1PDF-P'(D)P(D)2FAgain…

Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) - 8 cos(0) = Enter your answer as a reduced…

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Q: conver the Following differential equation into a Perfect equation and then find 1+5 general…

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Q: Thank

A: We will solve the problem.

Q: If s(t) 813 122-48t6, where t2 0 represent the position of a particle traveling along a horizontal…

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Q: A rocket is fired vertically upward from the ground. The distance in feet that the rocket travels…

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Q: Calculate the line integral of the vector-function F(x, y, z) = (y² +2²) i-yzj + xk along the path…

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Q: f(x) = xlnx

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Q: ind the general Solution of the of the following differentia yu-5y" +4y=013 y=0

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. O…

A: Answer: True

Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

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Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it dx dr dr d.…

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Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: Find the linearization of the function f (x) 1 9x+8 at = -1. L(x) = -9x-10 si Find the true values…

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

Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: USING WASHER METHOD Find the volume of the solid obtained by rotating about the y-axis the region…

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Q: Find the solution of the given initial value problem. 9 cos t y' y = y(π) = 0, t-9, t> 0 y(t) = =

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Q: d. dx 2√x+3+x

A: Given,∫12x+3+xdx

Q: 4. 2-5 2 -1

A: Given: ∆=|2-52-1|

Q: What is the solution of the given ODE * xy' + y = √x /2 x = {√x + ² y = {√x + = 2 y 1 x Option 1…

A: Given problem:- What is the solution of the given ODE*   xy' +y= √x

Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

A: We have to draw the direction field for the given differential equation.

Q: Set up the iterated double integral in polar coordinates that gives the volume of the solid enclosed…

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Q: convert the following differential equation into a Perfect equation and then Find its general…

A: Given problem:- convert the following differential equation into a Perfect equation and then Find…

Q: Given: Let B (x, y, z) = (xz, yz, 3x² - z²). 1. The task is to identify the work done by B on a…

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Q: =: Triangle may not be drawn to scale. pose a = 3 and b = 8. an exact value or give at least two…

A: Please refer to the image below

Q: Solve. 1. Find the equation of the family of curves whose slope at any point (x, y) is 3x. 2.…

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Q: क्ने Find the curl of F(x, y, 2) = (2x,3y, 52). depends on the point (x, y, z) ● 10 O

A: Let's find curl.

Q: b). Using an appropriate triple integral, evaluate the volume of: [Verify using Mathematica 1). ii).…

A: We have to find the volume.

Q: d. dx √2√x+3+x e. S da x√4x + 1 f. dx x√4x²+1

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Q: Evalu‎ate ∫C (x + 2y) ds, w‎here C is the cu‎rve defi‎ned by y = √(4 − x2), for x ∈ [0, 1]

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Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 6x² + 11x − 6 on the interval…

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Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it da da d. +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ¹In(1 + x) -dx X

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Q: 4x Compute the values of dy and Ay for the function y = e + 3x given x = 0 and Ax = dx = 0.02. Round…

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Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: USING CYLINDRICAL METHOD Find the volume of the solid obtained by rotating about the y-axis the…

A: Given that, Solid obtained by rotating about the y-axis the region bounded by y=2x2 - x3 and y = 0

Q: In Exercises 1 and 2, compute the solution of the given IVP. d²y 1. +9y2 cos(3t), y(0)=2, y'(0) = -9…

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