Determine whether the following sequences are convergent or divergent. If a sequence is convergent, find its limit. (a) an = n – - n

Q: The length of an arc of a circle with a central angle of 120° is 6r cm Find the radius of the circle...

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Q: Problem 1 (a) Solve the differential equation y' - 4xly = - 3x6 (b) Find the solution of the initial...

A: a.Solution :y'-4x-1y=-3x6dydx-4xy=-3x6this is a linear diffrancial equation in the form dydx+Py=QI.F...

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Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

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Q: 10. Given the curve: y = 4cos°x – 3cosx, find the following values of x (from 0 to 2pi radians) when...

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Q: ... Select the correct choice below and, if necessary, fill in the answer box(es) to complete your c...

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Q: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

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A: maxima minima question, if it is helpful, like and thumbs up.

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Q: cos x(2 + sin x)$ dx

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Q: Determine the average value of the piecewise function f defined below on the interval x -2 to x = 3....

A: We have to find average value of given peace wise function.

Q: Use the definition of convergence to prove the given limit. sinn lim n00 sinn How can you prove that...

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Q: 5 and g(x) = Let R be the region bounded by the functions f(x) = 3x? shown in the diagram below. Fin...

A: Graph of the region is given, we have to find its area

Q: Find f'(x). f(x) = In x +3 eX – 4x² %3D

A: f(x)=lnx+3ex-4x2Differentiate with respect to xf'(x)=ddx(lnx+3ex-4x2)=1x+3ex-(4×2)x=1x+3ex-8x

Q: 3-4 The figure shows a lamina that is shaded according to the given density function: darker shading...

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Q: Given vectors u = (-7, –5) and v = (2, –2) , find the difference V – u and represent the difference ...

A: Please refer to the solution which is uploaded in step 2

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: etermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that...

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Q: If h(x) = f(g(x)) and f(1) = 7 f'(1) = 10 g(1) = 1 , and g'(1) = -5 find W(1) О 350 O Not enough inf...

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Q: 25. Find the volume of the solid that is enclosed by the cone z = Vx² + y? and the sphere 22 + y? + ...

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Q: armer finds that if she plants 90 trees per acre, each tree will yield 75 bushels of fruit. She esti...

A: Given query is to find the number of tree per acre to maximize the harvest.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j...

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Q: A tank has 150o liters of water in it at time t = 0 hours. Water begins to be pumped into the tank a...

A: Explained below 

Q: Use implicit differentiation to find y' and then evaluate y' at (- 2,0). - 32 ey = x5 - y3 y' = D y'...

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Q: sketch the curve x2 + x2y2 = a2 y2 , a> 0. Enumerate the steps in your solution

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Q: 3-4 Change from rectangular to cylindrical coordinates. 3. а. (4,4, —3) Answer + b. (5/3, –5, v3) An...

A: To Convert Rectangular coordinates (x,y,z) to Cylindrical coordinates (r,θ,z) :           As x= rcos...

Q: Prove using elements that for any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr...

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

A: To determine whether the lines intersect, and if so, to find the point of intersectionx3=y-2-1=z+1, ...

Q: Evaluate the limit: limx→0 √6x+64−8/−4

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Q: Determine is the series is absolutely convergent, conditionally convergent, or divergent. Show your ...

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Q: (A) Estimate the area under the graph of 5 f(æ) = - from x = 1 to x = 6 using 5 approximating rectan...

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Q: Solve y + 4y = e4* y(0) = 2 %3D

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Q: Consider the following. u = 5i + 3j, v= 2i + 4j (a) Find the projection of u onto v. 44 88 20 20- (b...

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Q: The graph of f(x), shown here, consists of two straight line segments and two quarter circles. 22 Fi...

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Q: Find the indicated partial derivatives of: -8x 7y - f(x, y) 5а + 2у fr (x, y) = fy(x, y) =

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Q: A point starts at the location (4.5,0) and travels CCW along a circular path centered at the locatio...

A: Solution: According to question, the diagram should be like this

Q: ven the piecewise function defined below, determine the value of f (x)dx in simplest form. [3x? – 10...

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 14, (5, 5, ...

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Q: Find the linear approximation of the function f(x) = V1- x at a = 0. L(x) = Use L(x) to approximate ...

A: topic - linearization of a function

Q: plane passes through each X + 2y - 4z - 1 = 0 %3D (a) (-5, 1, –1) O Yes O No

A: Given query is to find plane passes through the point or not.

Q: A fence 20 feet tall runs parallel to a tall building at a distance of 4 ft from the building as sho...

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Q: The functions f and g are continuous and differentiable with g(x) = f'(x). Selected values of the fu...

A: Given query is to find the average value of the function g(x) over the indicated interval.

Q: Let R be the region bounded by the functions f (x) = 2: 4 and g(x) = 4x as shown in the diagram belo...

A: Given, y= 4x y= 2x²-4 Equating the above two equation we have, 2x²-4=4x 2x²-4x-4=0 x²-2x-2=0 x= (-b+...

Q: A point is moving on the graph of xy = 20. When the point is at (4,5), its x-coordinate is increasin...

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Q: What is the integral from 0 to 1 of the function f(x) = x? (Hint: think about areas)

A: Given function, f(x) =  x

Q: csc? 20 d0

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Q: considering that the rate of decay is proportional to the cube of the material

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Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

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