Consider the following series. 00 n = 1 1 x0.6 Evaluate the following. [ Use the Integral Test to determine the convergence or divergence of the p-series. 1 nº.6 dx = converges diverges

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A: Given: px=3x4-3x3-7x2 +x +2 To find: Rational and irrational zeros of p(x)

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A: Given Surface equation:- r→u,v=ucosvi→+usinvj→+uk→

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Q: 10) Analyze all ordinary and singular points for the following DE's. Must show all work! a) 2x(x -…

A: Please see the below picture for detailed solution.

Q: 12. fx²e-x dx 13. fx√x² - 4 dx 14. cos √t dt

A: The given integrals are;  13) x sqrt(x2-4) 14) cos[sqrt(t)].

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Q: it exists) integral (if it exists) Find the indicated integral (if ·∞ e4x e8x + 1 dx =

A: The given integral is e4x/[e8x+1], limit from -infinity to infinity.

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Q: Evaluate each integral. fæcos x cos(5x) dx

A: Integration by parts rule

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A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

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Q: Use logarithmic differentiation to find the derivative of the function. y = x6/x x²

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Q: 5-6 Find the area of the shaded region. 5. y = x³ - 3x (-2, 2) YA 0 (2, 2) y = x X

A: Application of integration

Q: 3. Differentiate the functions below. 5) y = (2x5 + 3)cos x²

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

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Q: The Sumeru Akademiya wants to manufacture Canned Knowledge in literal cylindrical cans that could…

A: Let h be the height of the cylindrical can and r be its radius.   Volume of cylindrical can can be…

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Q: During a walk-a-thon, Noah's time in hours, t, and distance in miles, d, are related by the equation…

A: The equation is given as , 13d=t where t is time in hours and d is distance in miles.

Q: Triangle ABC has vertices A(4, 7, 7), B(1, 6, 5), and C(–2, 9, 8). Which kind of triangle is ΔABC?…

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Q: Consider the graph f(x) = 1/x of in the first quadrant. Show that the segment of the tangent to the…

A: Solution: To show that the segment of the tangent to the curve in the first quadrant is…

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Q: The Sumeru Akademiya wants to manufacture Canned Knowledge in literal cylindrical cans that could…

A: a. The cost of production C can be modeled as: C(r, h) = 2πr^2(0.02) + 2πrh(0.01) Where the first…

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A: This is a question of curve plotting of the function for different value of c. Given equation is of…

Q: Let f be a function defined as f(x) = {₁/2²) Note that e≈ 2.72. The value of f'(4) is approximately:…

A: Given:  fx=xex2+8 if x<24x2x+32 if x≥2 To Find:  To evaluate f'4.

Q: 2 An object is moving with a uniform acceleration a = 2ms-², determine the functions for: a)…

A: We will find the required.

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A: We will find the required.

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A: ∫6∞ xe-x3dx

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Q: Find the area under the curve y = sin(t) area = cos(t) between t = 0 and t = π/2. Enter diverges if…

A: The region bounded by the curve y=costsint between t=0 and t=π2. We have to find the area of the…

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Q: line to the graph of y = g(x) at x = 4 is 4x+12y = -56 It follows that y = is the equation of the…

A: Given that at x=4, 4x+12y=-56 is a tangent.

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Q: Find dy/dx in terms of x and y if arcsin(x¹y) = xy¹. dy = dx

A: Solving the following problem

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Q: 6л Graph the set of points whose polar coordinates satisfy the equation 0= 7 бл Choose the graph…

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Q: Question 6 Determine the center of mass (x, y, z) of the homogeneous composite solid with a…

A: Determine the center of mass?

Q: tion about the origin. hat is the 13. Let T: R2 R2 be the linear transformation such that T(e₁) and…

A: Please see the below picture for detailed solution.

Q: Suppose f(x) = (x − 3)(x − 7)³ + 7. Find the absolute extrema of f on each of the following…

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Q: solve the following differential equation 1. (x2+ 1)y' + 4xy = 3x

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