Let r(t)=(3-2 cost)i + (2+2 sin t)j. Find the arc length parametrization in term of the arc length measured from the reference point given by t = 0. (b) Find the are length over the interval 0,7

Q: Find the solution of the given initial value problem. ty' + 4y = t² − t +7, y(1) = 2, t>0 Y

A: We know that a differential equation of the form y'+P(t)·y=Q(t) has Integrating Factor (I.F.) =…

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Q: The cost C of a product is a function of the quantity x of the product: C'(x) = x² - 3000x+50 .Which…

A: Please refer to the image below

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A: topic- definite integral

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A: Concept: The general homogeneous second order differential equation: y''+P(x)y'+Q(x)y=0 Regular and…

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A: Here we have to find the volume of the solid region.

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Q: Give the complete solution Find the derivative of f(x) = 5x6 - sec-1(x2)

A: Complete solution is given.

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A: If S is a subset of  R,   Then every set S  will always have an open cover.

Q: X=(1)+ wam (xf pulf Z-x7=(x)₂ + £I-E#

A: Topic = Integration

Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

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A: We have to find the population.

Q: Find the length of the spiraling polar curve r = 7e²0 From 0 to 2π. The length is

A: We will use the length formula of a polar curve on a given interval.

Q: Problem 4. (. Let C be the curve given by parametric equations r(t) = 1², y(t) = 2t, z(t) = ln t, t€…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Andy and Donald are both running toward the soccer ball during a game. Andy's path is represented by…

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Q: A balloon is released from the ground 100 meters from an observer. The balloon rises directly upward…

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Q: 2 . show that V(x,y) = x 'f (2x+y) is the general Solution of: av X du 2X 1 = V ду dx

A: To show that, vx, y=x f2x+y is the general solution of: x∂v∂x-2x∂v∂y=v

Q: (b) the volume of the solid B that lies above the cone z = 3r² + 3y² and below the sphere x² + y² +…

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Q: Directions: Use the diagram as a reference to answer the question below. x-axis h y-axis If arccos =…

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Q: Zxx-4Zxy-Zyy=0 Zxx+4Zxy+2ZyY=0 Zxx+Zyy=0 Zxx+6Zxy+9Zyy=0 Zxx-10zxy+26Zyy=0

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Q: Find the volume of a right pyramid that has a square base in the xy-plane. -1 ≤ x ≤ 1, −1≤ y ≤ 1,…

A: We have to find the volume of pyramid.

Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

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

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 3x)y², y(0) = = 2…

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Q: Evaluate the double integral over the rectangular region R. x√9 - x²dA R = Mi [[ x√√9 – x²dA; R =…

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Q: Are Lebesgue integrals always finite?

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Q: √ √ 1 √x² - 2x + 5 dx

A: Indefinite Integration

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Q: Directions: Solve the following using the theorems on differentiation. 1. Evaluate | 7e*dx 2.…

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Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: (t2 +2t) dx/dt  = 2x+2 ; x(1)=1. Find the solution of this initial value problem.   Here…

Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: Q1: A- Write the following algebraic expression in its simplest form: 5x+3x²+5x+6 X *+3 25x²-9

A: Please refer to the image below

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Q: DIFFERENTIAL EQUATIONS (Please answer ASAP. Solutions only. No long explanation needed. Rate will be…

A: To solve the differential equation.

Q: Q1/ Solve the initial value problem (IVP) of the differential equation by using the appropriate…

A: Concept: Initial value problem: An initial value problem is a difficulty in determining a function y…

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: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: 1. Evaluate a) for²dr, 2. Evaluate fr+7r² dr. 3. Evaluate a) fe²dr, r/2 4. Find sin rdr. b) dr, c)…

A: 1. evaluate  a) ∫01x2dx = [x3/3]01 = 1/3   b) ∫231/x2dx [-1/x]23 = -1/3 +1/2 = 1/6   c) ∫12x2dx =…

Q: Evaluate the double integral: 2 ਰੰਜਨ dA e3(x² + y²) R where R is the unbounded region between 0 ≤0 ≤…

A: Let's solve given double integration.

Q: Evaluate y' y = cosh²12x +sinh²6x

A: