Find the radius R of convergence for the series R = n=1 n! xn nº

Q: 49. Show that if x > 1, then ln x ≤ x − 1.

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Q: 7. Determine critical points for each of the following functions. 2 d. y = x² 32√x e. y = x³ + 3x² -…

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A: The given function is To find:-rootsdomian intervals for which the function is positive and negative…

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Q: Evaluate the integral: 0 x = (A) Which trig substitution is correct for this integral? Ox= 16 sin(0)…

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Q: Evaluate ff xdxdy where R is the region bounded by x=2, y = 0 and y = x

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A: By changing the variables, to evaluate the following definite integral.

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Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

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

Q: Determine the convergence or divergence of the series. (If you need to use co or -co, enter INFINITY…

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Q: Find the indefinite integral and check the results by differentiation S(4x²+ + 3)²dx

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Q: The system of differential equations : has the solution Y C₁ et V₁+ C₂ e¹₂ V₂ + C3 e¹³ V3 where (in…

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Q: Give the negations: All cars run on a gasoline

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Q: Find the integral. Use C for the constant of integration. | (x² (y² + 3)² dy

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Q: 4. n=1 ne-n

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Q: The Taylor series for f(x) = x³ at-4 is cn(x + 4)". Find the first few coefficients. Co= C1 = C2 -…

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Q: Two cylinders are given. The larger cylinder is a dilation of the smaller cylinder. Part A:…

A: Smaller length = 2mLarger length = 9mVolume of the smaller cylinder = 24 pi m3

Q: 2x - 5y = 7 3x + 2y = 4

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Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y₂ = −4y₁ + 1y2 where y₁ (0)= 4, y2…

A: The objective of the question is to verify if the given functions y1(t) = (4 - t)e^(3t) and y2(t) =…

Q: 8. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval [0, π/2], are…

A: The given functions are The functions f and g considered to be orthogonal on interval  if

Q: Highest point on the major axis: (2,11) Lowest point on the major axis: (2,-1) Rightmost point on…

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Q: A company's marginal cost function is C'(x) = 686 - 4x +0.06x² where x is the number of units, i…

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Q: Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function.…

A: Horizontal asymptotes of the rational function:Vertical asymptotes of the rational function: The…

Q: Find the sum of the series: n=0 (-1)"49"+2 n!

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Q: (11,20) (11,20) Show that (40) fdx+ gdy = f(4,1) 24x²y³dx + 40y^³dy is independent of path: J(4,10)…

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Q: Consider the functions f(x) = 6 arcsin (6x) g(r)= 12arctan (a) Find the derivatives of f(x) and…

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Q: A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.261)e1.12567t…

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Q: Given w = and ws. x² + y² + 6z Y x = sinp, y=p+ 3t - 4s, 2= t³ and p = 1-2t. Determine wt

A: Given that  ,

Q: The function f(x)=x^3 - 3x^2 - 9x D. Where is the function f(x) concave up or down? E. What are…

A: The given function is