Let {an be the sequence 100 Use MCT to show that {an}1 converges. an+1 = a₁ = 2, 1 3- an for n > 2.

Q: 1. Derive the expansion sin(2²) 11 -1% 22 1 22 3! + 5! 10 7! +... (0<=<∞0).

A: We shall use the expansion of sinx

Q: Suppose that the total cost (in dollars) for a product is given by C(x) = 1700 + 220 ln(2x + 1)…

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Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t2,    y = 3 +…

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Q: 14. Find the interval and radius of converence for 3x √n+1 n=0

A: The given series is:∑n=0∞ (-3)nxnn+1

Q: Given that f(x)= x12h(x) h(-1)=5 h(-1)=8 Calculate f'(-1):

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Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: 2. Determine the equations of all tangents to the relation (x-3)² 2²+2/2²24 4 = 1 where x = 2

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Q: Use technology to obtain approximate solutions graphically. All solutions should be accurate to one…

A: we use Geogebra to find the point of intersection of the line through (0,1) and (4.3,2) and the line…

Q: Determine the equation of the tangent line to the path r(t) = (sin(4t), cos(4t), 125/12) at t = 1.…

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Q: After substitution is performed, which of the following is equivalent to ſº (x² − 1) ª 2xdx? 10 ¹0…

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Q: 8 Ν n = 2 (-1)" Δη In(n)

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Q: Raggs, Ltd, determines that its MC, in $'s per dress, is given by C' (x) =- 2/25x +50 for X ≤ 450.…

A: Given marginal cost function C'( x ) = -225x + 50 Total cost from 0 to a is given as C( x ) = ∫0aC'(…

Q: π Compute the integral: S -TT sin t 1 + t -dt (Hint: sin(t) = - sin(t)) =I

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Q: For each of the following functions, solve the equation f'(x) = 0: b) f(x) = (Inx + 2x)^1/3 (…

A: since you have posted multiple question i can do first question as per our company guidelines.…

Q: The direction angles of a nonzero vector a are the angles a, ß, and y (in the interval [0, m]) that…

A: We need to find direction cosine and angles.

Q: Given z₁ and Z2, find the distance between them. Z₁ = -5-7i and Z₂ = 8-3i √[?]

A: find the distance between them Z1 and Z2

Q: Solve the initial value problem below using the method of Laplace transforms. w" - 8w' +16w=48t+200,…

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Q: The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial…

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Q: Question Evaluate the definite integral given below. Submit an exact answer. Provide your answer…

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Q: Find the gradient of the function at the given point w = x tan(y + z), (10, 3, -1) Vw(10, 3, -1) =

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Q: 5. Evaluate the indefinite integral 3x √x-1 -dx

A: let  D=∫3xx-1dxwe know→(i) ∫xndx=xn+1n+1+c

Q: A silver dollar is dropped from the top of a building that is 1353 feet tall. Use the po s(t) =…

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Q: JJ 18 17 16 15 14 13 12 11 10 10 9 8 7 6 5 12 4 3 2 2 3 4

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Q: 3) Consider the function g(x) = cos(3x). a. Write the first three non-zero terms of the Maclaurin…

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Q: Evaluate f -dx 3 x²+3x¹ x² 1

A: Integral

Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum. Then, use the test…

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Q: Simplify the expression by using a Double-Angle Formula. (a) cos² (37°) - sin² (37⁰) cos 74 (b)…

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Q: 5. The function y₁=+1 is a solution of (1-2-2³)+2(1+)/-2yy=0. Find the general solution.

A: PLEASE NOTE: There is a slight  typing mistake in this question ,the differential equation should be…

Q: A house increases in value in a linear fashion from $220,000 to $300,000 in 5 years.Find the…

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Q: Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) =…

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Q: Pollution levels in a lake have been modeled by the equation x = 0.03 + 0.18e−0.35t where x is the…

A: The given equation x=0.03+0.18e-0.35t, where x is the volume of the pollutants and t is the time in…

Q: -3 (-2,-2) -2 3 1- -1 -2 (1,1) 2 3 4

A: Equation of graph is fx=ax3+bx+c

Q: After substitution is performed, which of the following is equivalent to S² x√√4x²+9 dx?

A: To calculate ∫02x4x2+9dx.

Q: Find the domain of f(x)= Mostly sunny x|x€Rx‡¬ √10} 00 x|x€R_x#√10} Ox|x€R¸x*-√√10, 10}…

A: a2 - b2 = (a - b)(a + b)  and 10 = (10)1/2(10)1/2

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Identify the real numbers Xo X1 X2 X3 and X4 (a) f'(x) = 0 Oxo 0x1 0x₂ 0x3 X4 Onone of these (b)…

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Q: 3π Find the length of the polar curve r(0): -2 cos 0 where 0 runs from to 2

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Q: Q. 5 Does the function y = l x-2 l have an inverse? Select the best answer. Its inverse is y = l…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Consider the following function. f(x) = 8x² - 4x Find the limit. lim Az-0 f (x + Ax)-f(x) Ax

A: fx=8x2-4xTo find : Find the limit                   lim△x→0fx+△x-fx△x

Q: For the following polynomial function f(x)= x³ - 3x² - 2x + 2, find the lower bound within which all…

A: We have to find the lower bound of the interval in which the roots of the polynomial lie.

Q: Determine F'(x) when F(x) = 2√1+Pa =√₁² dt 1. F'(x) = 4x√1+x² 2. F'(x) = 3. F'(x) = 22² √1+x¹ 4x…

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Q: 1 x+12' Given f(x)= find the average rate of change of f(x) on the interval [9,9+h]. Your answer…

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Q: Let g(x) = 5x²-3. (a) Find the average rate of change from -4 to 5. (b) Find an equation of the…

A: Here we have a function g(x) need to find the average rate of change and equation of the secant.

Q: Find a formula for the exponential function if f(0) = 1/2 A. f(x) = 6(3x) C. f(x) = 3(1/12) X f(3) =…

A: Here we have values of a function at tow points, with the help of those values we need to find…

Q: Find the indefinite integral. (Use C for the constant of integration.) -3 (+²+3)³/2 dx

A: We have to integrate expression  -3/(x2+3)3/2 with respect to x

Q: 6. Evaluate the indefinite integral (3x² − 2)(x³ − 2x)dx

A: Need to perform the indefinite integral after simplifying the expression.

Q: Find all the zeros of the function f(x) = x² + 81

A: The function is fx=x2+81.To find : Find all the zeros of the function.

Q: |- −3x ln(x) dx; _u = ln(x), dv= -3x dx

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Q: 20. The parametric chain rule states dx II dy dt. Prove this statement. dx dt 21. Explain how the…

A: (20)

Q: Use the Limit Comparison Test to determine if the following series converges or diverges. 00 Hint:…

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