Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j + 7k osts/122

Q: V. Consider the power series +∞0 n=1 (x + 1)" +1 1. Determine whether the resulting series when x =…

A: We need to find convergence and radius of convergence.

Q: Find the volume of the given solid region in the first octant bounded by the plane 10x + 8y +20z =…

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Q: (b) The integral (2- (2-sin x)²dz represents the volume of a solid. Describe the solid.

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Q: The graph of f is given. Find the following or write d.n.e. if it doesn't exist. If a limit is…

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Q: A manufacturer has been selling 1800 television sets a week at $480 each. A market survey indicates…

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Q: Determine whether the following series converges or diverges. n² +1 Σ n² +n +8 n=2

A: We have to find the series is Convergent or divergent.  We can apply limit rule to check it.

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 22 - 2y? - 35 - -4…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question.

Q: Q3. Change the order of integration and evaluate * * dy dx.

A: To evaluate ∫04∫0xdy dx using the change of the order integration. From the limit of integration the…

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 3) is twice…

A: Given :The distance between point on sphere P to A is twice the distance from P to BA-2, 5, 3 and…

Q: Determine the following indefinite integral. dx X√ 625 + x 2 dx S- x√√625+x² (Type an exact answer.)…

A: We have to determine the indefinite integral ∫dxx625+x2.

Q: Solve the initial value problem. dy do y=0 +y=10 cos 0,0>0, y(x) = 1 THEE

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Q: Parameterize the plane that contains the three points (-2,-2,-2), (-12, 2, 12), and (0, 35, 30).…

A: To find the parametric equation of a plane containing three points (-2,-2,-2,), (-12,2,12) &…

Q: 1. S x² (x+1)4 - dx

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Q: i) Find the general term (an) of the sequence 3e-¹, 10e-2, 29e-³, 66e-4, 127e-5,218e-6, ... ii)…

A: The given sequence is;  3e-1, 10e-2, 29e-3, 66e-4, 127e-5, 218e-6, ...

Q: Determine the following indefinite integral. X 15-02 ex dx = dx, x < In 3 9- e 2x (Type an exact…

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Q: A car depreciates by 17% each year. The value of a $30 000 over time is modelled by the function v =…

A: The given data is: The value of a $30,000 over time is modeled by the function v=300000.83t To find:…

Q: 30. Paolo's wife Cristina is not happy about the play area he proposes to build for their children.…

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Q: Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60…

A: Topic:- exponential growth function

Q: Use power series operations to find the taylor series at x = 0

A: We have to find the Taylor series.

Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

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Q: docs.google.com This option Question * The domain of the function f(x,y)-- x+7-1 D={(x,y) ER² / x² +…

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Q: x²-x-5 x(x²-x-2) Evaluate - dx

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Q: = xn For the function f(x) = cos(x), write Newton's formula as n+1 = F(xn) = solving f(x) = 0. Type…

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Q: Find the exact sum of the following series In 32 3 5 ¤ In ( ² ) - — / 2 12 In 3 (²/²) - 1²/ 2 ○ In…

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Q: Calculate the arc length of the indicated portion of the curve r(t). r(t) = (3 − 2t)i + (1+6t)j +…

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Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

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Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Identify the increasing and decreasing intervals for f(x) = x + 5 X-4'

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Q: y = 16 X + x² at x at x = 4.

A: Given Equation :- y=16x+x2  Find the equation for the tangent line to the curve at x=4

Q: Find the equation of the tangent line to the function f(x) = ln(5x) at x = 8. (Use symbolic notation…

A: We have to find out the equation of tangent

Q: Sketch the graph of f ( x ) = 2x³ - 3x² + 3 , indicating the points of inflection and the intervals…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 5 sin(t). The initial…

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Q: 1) For each of the following tests, give an example and explanation of a specific series formula…

A: We have to explain the series and give an example.

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= (1 +5x)(3-2x)…

A: topic- derivative and equation of tangent line to function

Q: Find the slope and y-Intercept (if possible) of the line. (If an answer is undefined, enter…

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Q: The interest rate for a savings fund was 3.80% compounded semi-annualy for the first 4 years and…

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Q: i) Find the exact length of the curve y X y = 2 X + — ii) Find the exact area of the surface…

A: Let's find exact length and area of surface.

Q: Determine whether the following series converges or diverges. 2 9k +17 2 Σ k=11

A: Given Series   ∑k=1∞ 9k2+17k2To find: convergence or divergence of the series

Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by ro the cosine…

A: I have solved b part as asked.

Q: q+m (v) m Submit Question 2 1 -6 -5 -4 -3 -2 -1 -1 2 3 A 16 5 1 Find an equation for the graph…

A: General equation  m=AsecBv-c+d Now we need to find A,B,C and D

Q: IV. Determine whether the following series converges or diverges. Show your complete solution. +00 3…

A: To determine whether the following series converges or diverges.∑n=2+∞ n4-234n3+5

Q: From this graph, Find the volume around the X-axis (Use π = 3.14). y=x (0, 0) (1, 1) y=x² R

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Q: Given the following function, f(x) = -2x^3-9x^2+108x-10 , find: a) The critical numbers. b) The open…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: Consider the following function: f (x) = -1/2 x^4 +16x^2 -4 Determine f′(x) and f′′(x).…

A: Solve the following

Q: Find the slope and y-Intercept (if possible) of the line. (If an answer is undefined, enter…

A: The given equation is 7x-8y=8 We have to find the slope and y-intercept of the given equation.

Q: L3Q6. If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x). A.2x – 1 + log x B.2x – 1 – log x

A: Given; f(x) = 2x – 1 and g(x) = log x

Q: Use the functions below to find the given value. f(x) = x 2 8 g(x) = x³ (g¹¹) (-2) = |

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Q: Evaluate f x²-x-5 x(x²-x-2) dx

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Q: II) Let f be the piecewise function f(x) = x³ + 6x² + 8x x+2 1-x-2, -, x≤-1, x -2 -1 1 1) Sketch the…

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Q: i) Find the general term (an) of the sequence 3e-²,4e¯4,5e¯6,6e-8, 7e-10, 8e-¹2,... ii) Calculate…

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