Compare the values of the series A = n=2 and the improper integral B = 2 dx. 1. A B 3. A = B

Q: Given the series 1 1 - - 1 3 > Next Question + 1 9 - Does this series converge or diverge? O…

A: We will find the required.

Q: Given sinx: 119 169 144 169 119 169 144 169 12 and cos x > 0, what is the exact solution of cos 2x?…

A: Given  sin x = -1213 and  cos x>0. We have to find the exact solution of  cos 2x.

Q: Evaluate: 8 [² (8-4√x (8-4√√x) dx

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Q: Find f such that f′(x)=6/ root x​, ​ f(4​)=36.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: Given query is to apply rolle's theorem.

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

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Q: Find the degree three Taylor polynomial T3 entered at x = 0 for f when f(x) = 1 (4x + 1)1/2 1. T3(x)…

A: As we know the nth order Taylor's polynomials at x=x0 is given by:…

Q: Find the most general antiderivative or indefinite integral. You may need to try a solution and then…

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Q: . Find the area between the curvey = x² and the straight line y = 8x - 4.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

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Q: 2. When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01…

A: Given: Rate of increase of radius = 0.01 cm/min Radius = 50 cm

Q: 2. If f(x) = √2 +4x, find f(3) of definition x → f'(3) using the , derivative. If" (3) is the limit…

A: Let's find value of f'(3) by using derivative of definition.

Q: S* (x² − 4x + 4) dx ≥ 0

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Q: Determine whether the vector field F = 5y²i + (10xy + e²)j + ye²k is conservative: Yes O No Find a…

A: Given vector field is ........... F= 5y2i+(10xy+ez)j+yezk Since given vector field is conservative.…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: We need to find parametric and symmetric equation.

Q: 3. lim (x² 3x) = -2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Which one of the following integrals gives the length of the parametric curve x(t) = t², y(t) = = =…

A: As we know that length of the curve from a to b  L = ∫ab( dxdt )2 + ( dydt)2dtGiven  x = t2y = 2t 0…

Q: Differential Calculus Differentiate the following: • y = x5 - ex In(x) • y = 6ex - 7x ● • y = 2ex -…

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Q: = 3. (a)In each part, evaluate the integral; given f(x): f₂f(x) dx (ii) f₂f(x) dx (b) Integrate: f…

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Q: Find the most general antiderivative or indefinite integral. (8 + tan ²0) de (Hint: 1+ tan ²0 = sec…

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Q: Using the slope formula, find the slope of the line through the given points. (8,0) and (2,-4)…

A: Given query is to find slope of the line.

Q: Let f be a twice-differentiable function with derivative given by f'(x) = 4x³ - 24x². Part A: Find…

A: We have to find the x- coordinates of critical and inflection points.

Q: z Find the Taylor polynomial på for f(x) = xe at z = 2.

A: we have to find the taylor polynomial P3   for function f(x)=xe-x  at  x =2   f(x) = xe-x   ⇒f(2)=…

Q: Use the fact that ∞ 2 sin x cos x = n=0 ∞ to find the power series expansion of sin² x at x = 0. n=0…

A: Given the fact that 2sinxcosx=∑n=0∞-1n2nx2n+12n+1!.It is required to find the power series expansion…

Q: Use Stokes' Theorem to evaluate $ F. dr where C is oriented counterclockwise as viewed from above.…

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Q: For the sequence an = 2(an- its first term is its second term is its third term is its fourth term…

A: Topic = Sequence

Q: Kate starts a new business manufacturing bobble-head figures of Eagles players. Her initial cost is…

A: To solve the following problem

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (x¹)i + (5ye*)j…

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Q: (E) What is the form of the general solution to this differential equation?

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Q: E{sinh-t}

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Q: Find the solution to the initial value problem u'(x) = x²+16,u(0) = 2.

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Q: i) f x² sinx dx

A: Dear learner, As per the guidelines, We can provide the solution for first one only. Kindly post…

Q: dw For the given functions, (a) express t as a function of t, both by using the chain rule and by…

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Q: Calculate to sum of the first 99 terms of the following series:  8+24+72+216

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Q: Find f such that f′(x)=4x−9​, f(9)=0.

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Q: Compute the integral of the scalar function or vector field over r(t) = (cost, sint, 5t) for 0 ≤ t ≤…

A: To evaluate the given integral.

Q: Without graphing, find the x- and y-intercepts for f(x). f(x)=x² - 4x +3 *** Select the correct…

A: The given function is f(x)=x2-4x+3 We have to find the x-intercept and y-intercept.

Q: A ski run on Giant Steps Mountain in Utah is 1475 m long. The difference in altitude from the…

A: GivenA ski run is 1475m long and the difference in altitude from the beginning to the end is 350m.…

Q: Evaluate the integral. 1 S₁ √x (1+√√x) S 1 √x (1+√x)² dx dx=

A: We need to solve integration.

Q: Use a parametrization to express the area of the surface as a double integral. Then evaluate the…

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Q: Find the divergence of the following vector field. F = (5x²yz, - 4xy²z, -5xyz²) The divergence of F…

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Q: 2. Given x³ + y³ = 3xy, find the equation of the tangent line at (2/3,4/3). I'm looking for your…

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Q: Find an equation of the line having the given slope and containing the given point. 3 m=, (5,-1) ...…

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Q: 5 a. For f(x)=, find an equation for the secant line through the points where x = 2 and X X = 5. 5…

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Q: The differential equation e dy dx = y- tan(x) is linear.

A: NOTE: Refresh your page if you can't see any equations. . the standard form of the first-order…

Q: Find the Laplace transform of the given function by using integral definition. f(t) = ent

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Q: (a) Solve cach of the following differential equations using separation of variables. i. ii. 2.…

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Q: Find the following limits for f (x) lim f(x) = 0 x-4 If necessary, select the most informative…

A: Given query is to find indicated limit.

Q: Determine all solutions to the equation 2sin² x = 1 + cos x on the interval [0, 2п). 0 О X= X= л 5л…

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Q: 1. Let y = x² + 1 and y = −2x + 1. (a) Graph the two functions together on the same plane. Find the…

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