Verify the identity + 1+cos 0 1-cos 0 2 + 2 cot²0

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

A: Consider the series

Q: Calculate the derivative of y with respect to x, if x³/² + y-5/2 = 7. dy dx

A: Given equation, .derivative rules:

Q: Find the vertex form of the function. Then find each of the following. (A) Intercepts (B) Vertex (C)…

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Q: 1. Consider the second-order homogeneous linear differential equation, y"+p(x)y'+q(x)y=0 (a) Let y,…

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Q: Differentiate. f(x) = In f'(x) = X 6

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Q: Which polar coordinate pair corresponds to the same point as (-1,)? © (1,4) (1, ²) o None of the…

A: To find the polar coordinate pair that corresponds to the same point as .

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

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Q: Verify the following identities: 1. tan y csc y 2. 3. tan x sec x = sec y cos y sin x cot x sec x…

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Q: d) How long after 1950 will the value of the painting be $6 billion? year(s) (Do not round until the…

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Q: f(0) = ln(cos 0) f(x) = log5 √√5x+1

A: f(θ)=ln⁡(cos⁡θ)

Q: Find the local minimum of the function f(x), which is given in the graph below. -6 -5 + -3 -2 5 3 2…

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Q: 2. We found a solution y-sinx for the following differential equation. y"+y=0 a. Use Reduction of…

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Q: The velocity of a particle moving along a line is a function of time given by 79 v(t) = t² + 12t +…

A: The velocity of a particle moving along a line is a function of time is given by,   Find the…

Q: 1. 003 400 050

A: 2.

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = 5x cos xt…

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Q: 3. A student is completing a homework problem practicing the method of integration by parts.…

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Q: intercept (x, y) =

A: we have given function

Q: purchases a new car for $21,550. He makes a $6000 down payment and finances the remainder thro tized…

A: We have to find the monthly payment, amount and interest.

Q: Find the present value of $4000 payable at the end of 2 years, if money may be invested at 6% with…

A: Given data

Q: Find the derivative of the function. y=e22x

A: Find the derivative of the function.y=e22x

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic section 2x² -…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = 3 x intercepts…

A: Given, vertical asymptotes at x=-2 and x= 3.Given, x intercepts at x=4 and x= 6.Given, horizontal…

Q: 4. For each integer n ≥ 0, define In = [cos" (a) da. (a) Use integration by parts to prove the…

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Q: Ib 1b State the E, & definition of the limit, then use it prove lim (3x − 1) = 5. x 2 Note: express…

A: To state the definition of the limit, then by using it to prove .Note: Since the student has posted…

Q: Solve the following homogeneous differential equations a. y"-4y'+4y= 0 b. 4y"+²y = 0, y(0) = 2,…

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Q: Set up an integral that represents the length of the part of the parametric curve shown in the…

A: x=tcos⁡(t),y=t−6sin⁡(t),

Q: Winter FunⒸ has determined that the total cost (in dollars) for its west coast factory to produce…

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Q: The hyperbolic cosine function cosh x (pronounced ‘kosh’) is used to describe a catenary, the shape…

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Q: 5x+500 A garden shop determines the demand function q = D(x) = 20x +9 the number of plants sold per…

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Q: Let f(x) = 2e * +5 1+e=x The graph of is given below. Use the graph of f to determine the given…

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Q: Solve the following homogeneous diffe y"-4y'+4y= 0 »._4y"+л²y = 0, y(0) = 2, y'(0) = 0 x²y" - 2xy' +…

A: Given differential equationwhich is clearly a Euler Cauchy DE

Q: Write out the form of the partial fraction decomposition of the function appearing in the integral:…

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Q: Solve for x. 3x = 22 Select the correct choice below and, if necessary, fill in the answer box to…

A: The given equation is

Q: Multiply: (2+5i)(2−13i). Give your answer in complex standard form a+bi.

A:

Q: f(x)=x54x

A: Given that functionWe have to find the derivative of the given function

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. √13n an =…

A: To determine whether the sequence  converge or diverge.To find the limit if the sequence is…

Q: The velocity of a particle moving along a line is a function of time given by 79 t² + 12t + 27 v(t)…

A: The velocity of a particle moving along a line is a function of time is given by,   Find the…

Q: y = x ln x - x y = e ln x

A:

Q: 2c Find numbers a and b such that √a ax+b-2 lim x →0 1. Note: X express your solution based on the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: If the velocity function v(t) of an object is at its maximum, then the value of a(t), its A/…

A: We will find the value of acceleration.

Q: Set up an integral for the area of the surface obtained by rotating the given curve about the…

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Q: Find the first and second derivatives of the following. 1-4√√x+x³ (a) y = (b) y = 3x²e² Y (c) y = x³…

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Q: The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area…

A: The given curve equation is  ,

Q: For the given parametric equations, find the points (x, y) corresponding to the parameter values t =…

A: Given,

Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: -xs -X sec (3x) +C…

A: Given Indefinite integral as follows

Q: Solve the differential equation dy (y¹⁰x) dx Use the initial condition y(1) = 5. Express y¹¹ in…

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Q: 8. A = [₁ 2].B= 0 3 -5 1 2 4 3 -1 6 045 0

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Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: f(x)=x3x3+3;x=1

Q: Determine x = f(t) for dx (₁²+2t) = 2x + 2, t> 0; f(1) = 4. dt

A: To determine  for .

Q: Find the average rate of change of the given function on the interval [4,5]. h(x)=5^x2+7x−4

A: To find the average rate of change of the given function on the interval .