sin vn 2n Determine the convergence of the sequence an . If it converges, find lim an. BIU A E EV Format + v ... Font Font ... v

Q: 4. 7 (t) = (4t, –2t, /5 t) = (4t, -21, v5 ') %3D

A: This is a problem related to vector differentiation. Based on the general formula we can calculate…

Q: 1.0 5

A: We have to find out limit

Q: Express the following sums using sigma notation. a. 4 + 5+6+7+8 b. 6+ 12 + 18+24 +30 +36 c. 12 +22 +…

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Q: (1) Which equation could represent the circle that has the center at A = (-2, 3) and a point B = (6,…

A: Equation of circle centered at (a, b) is (x-a) ^2+(y-b) ^2=r^2 Where r is radius

Q: Find the limit. Use T Hospital s cos(x) lim - sin(x) + 1- x- (1/2) os (27) CoS sin(2n) 1- 0.

A: Given query is to find the limit of the expression.

Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: Q1\ Differentiate the following x+1 2)y = ln- x-2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: A region is enclosed by the equations below. y = 8, 3 x = 1 z + 4' Find the volume of the solid…

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Q: f(x) = (13 + 6t² + 1) dt

A: SOLUTION-

Q: 2) Find the absolute maximum and minimum values of f, if any, on the given interval, and state where…

A: We know that for absolute maxima and minimum value we do derivatives. We know that derivatives of…

Q: 18. Find a geometric power series for f (x) 3 centered about x = 2. Write the first four terms. 7-2x

A: Let's find.

Q: Let u = (3,-2), v = (-2,5), and w = (0,1). Express 10u-4v+w in the form (a,b). 10u-4v+ w= (Simplify…

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Q: The variables x and y satisfy the relation 2 = 31-2x. (a) By taking logarithms, show that the graph…

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Q: Ing light is located 10 feet from a wall. The light completes one rotation every 3 seconds. Find the…

A: From the given data: Here, the complete 2π rotation is done in 3 seconds.  So, dθdt=2π3 rad/sec

Q: f(x)=x^3+6x^2−63x+6 A. interval [-8,0] 1.Absolute Max= 2.Absolute Min=  B. interval [-5,4]…

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Q: Determine whether n+1 converges or diverges. Give reasons for your answer.

A: Given: Here, an=n+1n2n. Notice that an=n+1n2n≈1n32. Now,                  limn→∞n+1n2n1n32=limn→∞…

Q: Cualuate indfin te ntaen Jett dt

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Q: Let F(x) = f(x*) and G(x) = (f(x))* . You also know that a? 5, f(a) = 3, f'(a) = 3, f'(a*) = 9 %3D…

A: Given that,F(x)=fx3 and Gx=fx3

Q: For the given points A, B, and C find the area of the triangle with vertices A, B, and C. A(4,7,2),…

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Q: Using the Alternating Series Remainder Theorem, determine the number of terms N required to appro…

A: Given problem:-

Q: 3) Find the sum of the first 12 terms of the geometric sequence -3,-6,-12, -24, ..

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Q: Find the limit. Use l'Hospital's Rule where appropriate cos(x) – 1 + lim 3x4

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Q: Find the roots of the following equation x6 – x – 1 = 0 Using an initial guess of xo =1.5 ?

A: We have to find the roots of the given equation.

Q: V1 + x 8. 1- x

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Q: Suppose that f(x)=2x^−4+5x^−2 Evaluate each of the following: 1. F' (2)= 2. F' (-1)=

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Q: Find the explicit formula of an arithmetic sequence with the given pr d = 12, and a6 = 68 %3D %3D

A: Topic:- sequence and series

Q: Solve the differential equation:+ y = e-* sin x 2

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

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Q: (3) In 2014, the United States Postal Service charged $0.48 to mail a first-class letter weighing up…

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Q: Suppose p(t) = - 0.36t° + 1021 + 6072t + 70,000 is the population of a city t years after 1994. a.…

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Q: Solve 1Ge follouing disferential eguatiug 2 dy ty= elx xy メー1

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Q: To create a college fund, a parent makes a sequence of 18 yearly deposits of $1100 each in a savings…

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Q: Find the critical numbers of f(x)=x^2−26x+3 and classify all extreme values, given that 0≤x≤15 .

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Q: Find the indefinite integral and check the result by differentiation. (es + sec?e) de Step 1 To find…

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Q: Given r = e-, find the following. A Determine the derivative in terms of 0. Show each step and…

A: First we find dy/dx

Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: Find the length of the curve y = xVa 0 <x < 1.

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Q: 1 to z = 6 using a Left Endpoint Approximate the area under the curve graphed below from z =…

A: Follow the procedure given below.

Q: Find all critical points of the function f(x) = x³ - x? – 54x + 6. (Use symbolic notation and…

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Q: A construction worker pulls a five-meter plank up the side of a building under construction by means…

A: Explained below

Q: Find the arc length of the graph of r(t) = ev#ti + e¬V%tj+2tk, 0<ts v2In 5 NOTE: Enter the ezact…

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Q: (Use decimal notation. Give your answer to three decimal places.) rate: 1.2 m/s

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Q: 1 11. Use the alternate series test to determine if E=1(-1)"+1, converges or diverges.

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Q: J-4) dx. Use the definition of the definite integral to evaluate

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Q: If f(x) = [(1³ + 6r² + 1) dt

A: Here, the given function is: f(x)=∫0xt3+6t2+1dt...(1) Note that, the Fundamental Theorem of Calculus…

Q: Q2\Find the point at which the tangent to the curve y = v4x² + 1 – 2 a)find the equation to the…

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Q: (CLO-1) Three players (Ady, Brenden, and Cara) are sharing a pie that is worth $15. Suppose that the…

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Q: Show your solutions for each of the questions in the following. Evaluate each indefinite integral.…

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Q: Find exactly T() and N() for x- e'cost, y = e'sint, 2- e' for : - 0. [Choose the correct answer.)…

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Q: Write the sum using sigma notation: 9+ 13 + 17 + 21 + ...+ 57 = B, where n=1 A = B =

A: Topic:- sequence and series