If bn = determine whether this sequence converges or 271 Convergent, give the limit of this sequence. diverges. If

Q: 3 x dx + 5x² (4²5) ³ - dy4 Determine the order and degree of the differential equation, 3x - xy = 0.

A: Determine the Order and Degree of the Differential equation.

Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: which is what in decimal form?

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Q: Find the exact length of the curve. 1 y² = 16(x + 1)³, 0≤x≤ 3, y>0 109/109 (217 217 (21717 X

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Q: Find a unit vector in the direction in which f(x, y, z) = Z increases most rapidly at P(1, 2, −2),…

A: The function is given by fx, y, z = xz+zy2 The point coordinates of point P is 1,2,-2 To evaluate:…

Q: In 2004, an art collector paid $59,886,000 for a particular painting. The same painting sold for…

A: To find out the exponential growth rate and also the exponential growth function.

Q: Suppose f f(x) dx = 25, f f(x) dx = 10, f g(x) dx = 10 and h(x) = 0 3 the following: a. (5f(x) 6g(x)…

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: Find all values of n such that y = x" satisfies x²y" - 20y = 0

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Q: Consider the function f(x) = 3x²-5x+2. Use it to find f(4), f(-1), and f(a + 3). f(4) = 30 O…

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Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy B.…

A: we need to find out at which of the equations has solution of the form F(x,y)=c

Q: Find the area of the shaded region. r² = sin(20) 4

A: See this solution in below.

Q: Evaluate the following integral. 9 4 dx 1-√√x

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Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: (b) Let y = (2x + 1) cos. Compute by using logarithmi dy dx

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Q: Three hundred books sell for $40 each, resulting in a revenue of(300)($40) = $12,000. For each $5…

A: Given: Price per book = $40 Resulting revenue was (300)($40)=$12,000 For each $5 increase in price,…

Q: Find the general form of f if f'(x) = 10f(x).

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Q: A central angle in a circle of radius 8 is subtended by an arc oflength 10pai. Find the angle’s…

A: Given: Length of arc, l=10π units Radius , r=8 units To find the central angle’s radian and degree…

Q: ch of the described curves, decide the an equation for the curve. (a) A line through the origin that…

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Q: 5) Square PQRS with side length x is subdivided into four triangular regions as shown such that area…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the general form of f if f'(x) = 5f(x).

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Q: graph each function using the techniques of shifting, compressing or stretching, and reflections.…

A: Given, hx=2x-1

Q: II. Give the indicated derivative 1) find the 27th derivative of cos x

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Q: Generate differential equation by elimination of arbitrary constants. 2. y=x+c₁e* + c₂e-*

A: Given: Now,    y'=x+c1ex+c2e-x' =1+c1ex-c2e-xy''=x+c1ex+c2e-x''=c1ex+c2e-x

Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: 1. y' + ytanx = COSX; y(x) = (x + c)cosx; y(π) = 0

A: y'+ytanx=cosxy(π)=0proove that  solution isy(x)=(x+c)cosx

Q: Determine the solution of the differential equation: (3tanx-2cosy)sec²x dx + tan x siny dy = 0

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

Q: a. Graph the functions ƒ(x) = x/2 and g(x) = 1 + (4/x)together to identify the values of x for…

A: Given:-f(x)=x2g(x)=1+4x

Q: 1) Determine whether or not the following equations are exact

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Q: (Question-Solution-Final Answer-Conclusion format) E. Generate solution of the first-order…

A: The solution of given exact differential equation is as follow.

Q: If f(x) = f'(x) = f'(2) = tan x 2 sec x 1 + 2 tan(x) sec(x)

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: Which of the following equations OA. (2x sin y + y)dx + (x² cos y + x)dy = 0 OB. 1 dx-dy-0 y O E.…

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Q: 2. 8[][

A: The objective of the question is checking the convergence or divergence of the given series.

Q: Solve below given differential eqn (x3+ уз) dy xe²4.de

A: We need to solve the differential equation.

Q: Find dx dx || by implicit differentiation. 6x² + 7xy - y² = 8

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

Q: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 18. The cross-sections…

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Q: O D. dependent variable = y, second order, first degree, not linear

A: The given differential equation

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: The figure shows the positions of an object as a function of time t. S 10 J540 501 + 20 30 40 50 t…

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Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

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Q: Evaluate the following integral. dx √√x². + 2x + 122 What trigonometric substitution will be the…

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Q: Find the interval of convergence of the following series Σ(-1)₂(x - 2)n n5n n=1

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Q: I need to find the integral of [math]\frac{\cos(2x)}{\cos^3x}[/math]

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Q: If f(x) = f'(x) = = f'(4) = 3 tan x, then -sin(x) - 3 sec²(x) COS X >

A: we need to find out the derivative for the given function

Q: 3. Consider the initial value problem y′ +y=1-², y(0) = 30› where yo denotes some real constant. (a)…

A: To find the solution of given differential equation.