Use series to approximate the definite integral I to within the indicated accuracy. 1/2 x arctan(x) dx (four decimal places)

Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x? N(x, y) = x² - 2y (I): (2xy – 3x )dx…

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: 2x dx e 2X-1

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Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value.

A: Topic = Algebra x=3

Q: 8. Describe the steps you would use to determine the absolute extrema of the function Ax) = (x- 3)e"…

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Q: Q2) Find the integral of: 6 tan*x dx

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Q: e2 º In(2) dzr

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 ||M(t)||* 15: r(t) = t’i + tl5j K(t) =

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Q: X+3 Q4) Find the integration by using: J: dx 2x3-8X

A: This question is based on indefinite integral.

Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: 3. S- dx 1-sin'x

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Q: Given a differential equation dx with the initial condition, y cos (2x) 8

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Q: 1 æ(ln æ)² de

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Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B

Q: 1. 5x²+4x2-5 dx

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Q: Consider the following. z = x2 + y2, x = 4s + 8t, y = s +t az az and as Find by using the chain…

A: Here, the given functions are: z=x2+y2, x=4s+8t, y=s+t So, z is a function of x and y and x and y…

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Let y=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: 2. S CoSx+sinx-1

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Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: Describe the graph of the equation. r =-18i+(1-j+:k O Itisa parabola in the plane: = -18, with…

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Q: S cos³ 3x dx

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Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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Q: In(x) -dr

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Q: 5x3+4x2-5 dx

A: Use power rule integration technique

Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: d d Calculate ri(t) · r2(t)] and dt x r2(t)] first by differentiating dt the product directly and…

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Q: xdx 41. 12-х

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: 3 Consider the function g(x)= sin --1| with restricted domain [0,4]. Find and identify any relative…

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Q: The following series is divergent: (8")(10") (7")(9")+1' n=1 Select one: O True O False

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Q: We want to fenca in a ne slide b up againd a lacae building and Idbesn't noedh fancing rechanguler…

A: This question can be solved using the concept of maxima or minima.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: y = x(x2 – 4)

A: We have to find the area of the shaded region.

Q: ( sec(Inx) tan(lnx) dx

A: ∫seclnxtanlnxxdxLet u=lnx.=∫secutanudu=secu=seclnxAdd a constant to the solution=seclnx+C

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: What is the lim,→1 4x 7 .? x+1

A: limx→1 4xx+1The function is defined at x=1.limx→1 4(1)(1)+1limx→1 41+1limx→1 42=2

Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 13 9ts r(t) = e"i+etj K(t) :

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: Question 5 Consider the exact first order diff. equ: M(x, y) = 2.xy –3x? N(x, y) = x² - 2y (I):…

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Q: Apply

A: We will solve the integration.

Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Find div F and curl F if F(r, y, z) = xz'i+ 4y*x*j+ 62²yk. div F= curl F=

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Q: partial fractions to frd use 2 |- x9 + x8 2 3

A: Using partial fraction solving the given integration.