Find the radius of convergence and interval of convergence of the series. I need help with this problem

Q: Consider the function Z = 2x²(1 – e-y) where x and y are given to be 1 and In 1 respectively. Find…

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Q: 4. dy - (x-y+ 1)'dx = 0

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Q: Problem : Find the derivative of the series 2x 4x2 8x3 16x4 32x5 f(x) =1+ 1! 2! 3! 4! 5! Also show…

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Q: 9. sin“ x cos“ x dx

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Q: dy 1+y+1

A: We know. ∫xndx=xn+1n+1 for any real number n. ∫dxx=lnx

Q: The series > cos" (2) is divergent. n=1 This statement is true by the test for divergence. This…

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Q: dA when r = 2. dt dr Let A be the area of a circle with radius r. If = 2, find dt

A: Area of the circle with radius r is given by;A=πr2differentiating w.r.t time,dAdt=2πr drdtWhen r=2…

Q: A culture initially has 700 number of bacteria. At 1=5 hour the number of bacteria is measured to be…

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Q: - 4

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Q: y =-x (b) Use it to project the vector v =

A: Given

Q: Which of the following parametric functions create this graph? -4- -2- -2 2 -2 -4. x (t) 4 cos(t)…

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Q: Find the derivative of the following functions from first principles. (i) x (ii) e* (iii) log (x+ 1)

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Q: Answer(8) Linear First Order D.E. Solve the following differential equations of 1-e" dx +2(xe" -…

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Q: The functiong is defined as follows for the domain given. g (x) = 2x-1, domain = {-3, –2, 1, 5}…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: I am attaching image so that you understand each and every step.

Q: pleasee answer C and E

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

A: We can find the value of a and b as below.

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Given the following parametric equations, convert to rectangular equations: x = t + 5 and y = t² –…

A: Topic = Algebra

Q: (-1,3) -2,1) (0,1)

A: Topic = Functions

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

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Q: SIn?C3x) +C 4

A: To find the missing value in the integral expression.

Q: = सितो 11

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Q: 3. y = tan (3x)cot (3x)

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: 12-2t+tcos(t)-tet-4t2 Given a velocity function v(t) with initial condition s(1) = e, find the…

A: Given query is to find the position function.

Q: Which of the following is the correct definition of the limit? The lim f(x) = A, if and only if, for…

A: Explanation of the answer is as follows

Q: Given the differential equation x+2 2y ? find the particular solution, y = f(x), dæ with the initial…

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Q: 2 sinh x 2. Calculate the integral, dx. 5+6 cosh x

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Q: Integrate the ff.

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Q: Y1 = x² + 2x + 1 Y2 = 2x + 26 dx y2 35 30- 25 20- y 15 10

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Q: A. Determine whether the following functions are continuous or not. are not, classify them as…

A: Given : f(x)=x2-36x+6     To Find : type of discontinuity   Note : If f(x) is undefined at x=a, and…

Q: 7) Find the radius of convergence and interval of convergence of the following series: (х — 2)" | n²…

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Q: An isosceles triangle has one vertex at the origin, with its other two vertices above the origin and…

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Q: c. f(x) = (-1 if x 0 %3D

A: We need to find possible points of discontinuity.

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: State whether each of the following series converges absolutely, conditionally, or not at all. n²…

A: A series ∑an is called absolutely convergent if ∑ an is convergent . Limit Comparison Test :   If…

Q: SEATWORK Solve two problems; one problem from #1 and one problem from #2. Submit clear and upright…

A: A→=-1, 2, 3A→=1+4+9 =14B→=4, -3, 1B→=16+9+1 =26a)=A→B→ -B→A→=14(4, -3, 1) -26 -1, 2,…

Q: A toy manufacturer's cost for producing q units of a game is given by C(q) = 1420 + 3.6q + U.U00 the…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: Evaluate the following limit: lim (7,y)→(0,0) 5æ6 + 6 sin°(y) 14x6 + y6 3 4 11 15 2 3 The limit does…

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Q: A. r(2000) B. r(2000) – r(1991) r2000 C. S1901 r(t)dt r(2000)–r(1991) D. 2000–1991 2000 E. S1991…

A: We have to match the expressions.

Q: 2. Use the Closed Interval Method to find the absolute maximum and absolute minimum values of f(x) =…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

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