Test the series below for convergence using the Ratio Test. n + 5 54n +2 n=1 The limit of the ratio test simplifies to lim f(n)| where n 00 f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Select an answerv

Q: Vn Σ: 4n2 + 9 n=1

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Q: 2. On the wall of Mr. Piamonte's house, a 6-meter picture was hung so that its location is 5 meters…

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

Q: 4. dx = Inlx -e* +C %3D 5. S 2+3*dx = 4 6. Inlxl + C

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Q: (i) (x² + 1) tan-'x – x (ii) x³ loga x + e* cos x d (iii) e2 In cos 2x iv) 102 In cos 2x dx

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Q: value of n

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Q: 13 |xsin xdx ーT 15 (xsin xdx

A: I=∫ x sinx dxIntegration by parts;u=x, v=sinxI=x∫sinx dx-∫(1 ∫sinx dx) dxI=-x cosx +∫cosx dxI=-xcosx…

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Q: na "rx) ax = 7, evaluate Given dx - 0 dx. dx dx. (c) dx. (d) 3(x) dx.

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Q: Two lines with slopes m1= 4/3 and m2= -7/2 intersect at (3,2). Determine the equations of the two…

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Q: J (3vx +) dx = *+ 3) +° si- dx = In\xl - e* + C 3. 4. E. x2 %3D (鼎) 「(回-dx=n F. 2V 5. S 2+3* dx = 4…

A: Note:- As per your demand we solve question 4,5,6 for you  Given problems:-

Q: Jxcos(nx)dx 78 2л 80 |sin nxsin mxdx

A: 78. Find ∫-ππxcos(nx)dx Solution: If fx is an odd function and continuous at: -a,  a then ∫-aafxdx=0…

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Q: A beacon that makes one revolution every 7 seconds is located on a ship anchored 2 kilometers from a…

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Q: ا وا ور باه واه С. x e

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Q: 4. Consider the function f(x) = (2x - 3)5. Discuss the continuity and %3D differentiability at x =…

A: 4.f(x) = (2x-3)15 from the graph, f(x) is not differentiable at x=32 , since slope changes at x=32…

Q: In each case, determine whether or not the lines have a single point of intersection. If they do,…

A: A)x=5t, y=2t-1, z=3t-3x=t-6, y=-t+5, z=t-9finding common t;5t=t-6, 2t-1=-t+5, 3t-3=t-9t=-32, t=2,…

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Q: Use l'Hôpital's Rule to find the following limit. 5 sin (x) - 5x lim 2x3

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Q: S(-0) dx = - 4 In|x| + C 8. 2. )dx = 6 Vx + C

A: ∫x4-dx=x28-4ln(x)+CApply the Sum Rule:…

Q: review Activity 1.2.1. Suppose that g is the function given by the graph below. Use he graph in…

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Q: solve the following system x-y-z=0                                           x-y=z=2…

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Q: O f(x) is both injective and surjective.

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Q: Solve each equation. 0. -5 -5 1) -1 %3=

A: Here we have to solve, -504-1Z=-55

Q: Consider the points A(1,-1, 4), B(2, –3, 2), C'(-1, –2, 2), and D(4, 3, -6). (a) Find the volume of…

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Q: 2. Find the solution(s) to the differential equations: a. y"(x) + y'(x) - 6y(x) = 0 and b. y"(x) -…

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Q: Find the area of the shaded region. f(x) = x – 8x° + 21x, g(x) = 20x + 50 3

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Q: 6. Evaluate the integral ex e* +e-xdx

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Q: Consider the parallelepiped with adjacent edges u = 2i + 4j + k v = i + j+ 6k w = i + 2j + 5k Find…

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Q: 3X (x³+

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Q: Consider the graphs, shown below, of the functions f(x) (blue, first graph) and g(x) (red, second…

A: According to our policies we are allowed to give solution of only one question at time. For other…

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Q: 9. if A = [12 3; 4 5 6; 7 8 9], inverse of A is denoted by O A(inv) O inv(A)

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Q: B side of cube = 10 cm (A. B); (C. D); (E.G);(G.B) ? (Ex F); (A x G) dan (Cx F) ? 2. what is the…

A: From the given figure we get A→ = 10i+10k B→ =10iC→ =5j+10kD→=5i +10kE→ =10i+10jF→=10kG→=10i+10j+10k…

Q: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

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Q: Activity 1.2.4. For the moving object whose position s at time t is given by the graph in Figure…

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Q: What is the limit as x approaches infinity? What is the limit as x approaches negative infinity?

A: The given function is: fx=2x3+9x2-108x-5. The degree of the function is 3. So it is an odd degree…

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Q: 6. Find the area bounded by: d. The curves y=x-4, y38-2x.

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Q: Determine the absolute extreme values of f(x) = 5x – 10~/x on the interval [0, 16].

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Q: 2. y=2 x - x+ 3 x' + x? + 5 - 2x- 3. y

A: solution:-(2) y=2x2-x+3x-1+x-2+5dydx=ddx2x2-x+3x-1+x-2+5     =ddx2x2-ddxx+ddx3x-1+ddxx-2+ddx5…

Q: 6.26. у - Зxу%3D0

A: Topic = Differential equation

Q: 5. Figure below shows triangle AOC inscribed in the region cut from the parabola y=x' by the line…

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Q: To test this series for convergence n=1 nº +1 1 where p= You could use the Limit Comparison Test,…

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Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

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Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A: Given problem:- Find the point of diminishing returns (x,y) for the function R(x), where R(x)…