Find the radius of convergence, R, of the series. R = Î n = 1 I = n2n Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

Q: Given that 0. ∞ n=0 x = 1 1 <- x to x = = Identify its interval of convergence. The series is…

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Q: (2) Use a known Maclaurin series to obtain the Maclaurin series for f(x) = sin²x. (Hint: Use sin²…

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Q: 0/= log10 (x) dx

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Q: (e) Evaluate S 1+7x dx.

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Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

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Q: Let g(x) = = f(1) dt, where f is the function whose graph is shown below. At what value of x does…

A: Given: gx = ∫0xftdt Using Leibniz integral rule, we get g'x = ddxxfx -  ddx0f0 g'x = fx

Q: S 4sin x cos xdx I

A: topic- indefinite integral 2sinθcos(θ)=sin(2θ)sin2(θ)=1-cos(2θ)2

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Q: Given compute the following integral. Provide your answer below: -6f(x) dx = = 9 [² f(x) dx = 2,…

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Q: 2/4 + ²/81 + ²/1/729 t. Ⓒ274

A: 2.Solution:29+281+2729+.......29+292+293+.......this series is geometric series.Common…

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

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Q: s 32x² (x-15) (x+5)² dx I

A: Integral

Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: 04: Answer two only: (A): I A-2 1 -1 1-2 Find AB and AC.. -- 3 1 1 and 1 3 1 CO

A: Given :A=420210-2-11, B2312-2-2-121, C=31-3026-121

Q: 12. x² sin(x + y) = 1, -

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Q: J 24 tan3 xdx

A: topic- indefinite integral

Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

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Q: Find the particular solution of the differential equation given that, when x = 0, y =-4 and Q3 *…

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Q: If A, B, and C are 3×3 matrices; and det(A) = 5, det(B) = −2, and det(C) = 3 then compute: det…

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Q: 9. (x²-x+y) dx - x dy = 0 10. (2y² + 2y + 4x²) dx + (2xy + x) dy = 0

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Q: The owner of an apartment tower rents out each of her 250 apartments for the sum of $300 per month.…

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Q: 3. y = 2x² is a solution for which differential equation? 2y - y = 0 xy' - y = 0 2y'- y"=0 - y' -…

A: Given :y=2x2

Q: Find the general solution of the following differential equation. y" - 4y + 7y=0 NOTE: Use c₁ and c₂…

A: Given y''-4y'+7y=0

Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: (B): If A = 2i + 3j - 4k; B = 3i-4j+ 5k and C = i + j - k, find: (iv) (3A + 4B). C (1) A.B (ii) B.C…

A: The objective of the question is determine the addition and dot product of given vectors.

Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

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Q: • The orthogonal trajectory of the equation given below is already given. What is the value of "n"?…

A: The given equation x2+3y2=r2

Q: Sketch the function. 4 k(x) = -x² +6x²-8 Part 1 of 4

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Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t)i + sin(t)j + tk…

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Q: 9. TC/2 (3 sin² t cos ti+ 3 sint cos² tj + 2 sint cost k)dt

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Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: valuate the following double integral over the region R by converting it to an iterated integral. Se…

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

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Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…

A: Solution is given below:

Q: The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = π. dA = ( A =…

A: Here is your solution

Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

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Q: find the area of the triangel with verticies A=(0,0,0) B=(2,1,1) C=(3,1,2) round to 2…

A: This question can be solved using the concept of area of triangle using vectors.

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: The function g is related to one of the parent functions  g(x) = |x − 1| + 5 a.) Identify the parent…

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Q: The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R₂, R3, and R4,…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

A: The function is c(x)=2x2-12x+17. Then we have to answer the following... The graph of the function…

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

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Q: what about part (b) please.

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Q: B. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: Please see the answer below.

Q: Consider an exchange economy with 2 consumers, A and B, and 2 commodities, x and y. Each consumer is…

A: Multiple subparts are asked, I am answering first 3

Q: Q1/ Solve the following differential Equations. 3- dx +2²= 3x x

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