Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

Q: For each of the following series determine if the series converges or diverges. In(n) Σ n=2

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

Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: <press the area of the given surface as an iterated double integral, and then find the surface area.…

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Q: n2-2

A: Question number 5 is solved step by step. Solving more than 1 question is against the policy of…

Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

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Q: r=1+ 3sino

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Q: Find the interval of convergence for the Maclaurin series expansion for f(x) = e".

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Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

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Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

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Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

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Q: 'ind the area of the region that is enclosed by the cardiod = 20 + 20 sin 0. OTE: Enter the exact…

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Q: The Taylor series for cos(x) centered at a = 0 is given by: (-1)",2n (2n)! n=0 Using this result,…

A: Given problem:-

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. A 1 B) 4 C) 0.5 D 3

A: Solution is given below:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

Q: The position vector r describes the path cof an object moving in space. Position Vector Time r(t) -…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: Consider the following functions. f(x) g(x) 8 sin x %3D = 8 cos 2x -

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Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

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Q: The function ƒ (x) = |x| is continuous at every real number. %3D False True

A: Let's find.

Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

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Q: Question 13 Evaluate JJ xy dA , where R is the region in fa, 3) (1, (5, 3) R (2, 1) (4, 1) x A 56 В)…

A: A detailed solution is given below.

Q: af Find for the function: f(x, y) = xcos(xy) + 2xy2

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Q: Question 17 Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the…

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Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-2 and y=x about…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: given point. Function Point f(x, y, z) = V x2 + y2 + z² (10, 3, 9) %3D Vf(10, 3, 9) = Find the…

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Q: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

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Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

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Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: Fidn the sum: 2k (Write your final answer in fraction form, when applicable) A=31

A: Use the formula of summation then put the limits .

Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: Question 8 Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the…

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Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

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Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= &lt;0,-8,1&gt;+t&lt;5,0,5&gt;

Q: Question 7 Use double integration to find the volume of the solid. 3 3x + 2y + 4z = 12 A) 6 B) 9 c)…

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

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Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

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Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

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Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

Q: 1+9n² b) Determine whether the sequence a, = converges or diverges. If it converges, %3D 1+n find…

A: The given sequence is: an=1+9n21+n2

Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.