By Maclaurin series expansion, show that the sum of the geometric series may be written as a power series given by 00 aΣrn-1 = a + ar + ar² + ar³ +· ·+arn-1 +... n=1

Q: For items 22-23: The equation of a curve is y = 5tanx. 22. What is the slope of the tangent line…

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Q: bacteria culture starts with 200 bacteria and triples in size every half hour. After 2 hours, how…

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Q: writing the given quadratic s^2 +6s + 10 in the form (s+a)^2 + B^2 (that is to complete the square).…

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given po…

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Q: Find a potential function f for the field F = e²y + 52 (2 i + 4x j + 10x k). A general expression…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (1,4,5)…

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Q: Ashley heard that he could triple his money in 12 years if he invested it in a large…

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Q: In(3x) EXAMPLE 3 Calculate lim x → 00 SOLUTION Since In (3x)→ ∞o and In (3x) 1/x lim x → 00 = lim…

A: Topic = Limits

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

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Q: Question 5 fx²√3x dx is equal to 0 -27 (3 - a) 3 - -5 7 (3— æ) +15√(3-x) - + 2 2 -5 0 æ) −3 (3 – a)…

A: To find out the integration.

Q: [Select] 3x²+3 ³+3x-4 3x² +3 In{³+3-4} 1 ³+30-4 1 In{³+3x-4} 32-4) A. f'(2) 6.51 B. f'(2) = 1.5 C.…

A: Given function is  f(x) = ln(x3 +3x-4)  20) find derivative of f i.e. f'  22) find f'(2)

Q: Use Matlab Commands to solve the following exercises: Excercisel: a= b= Find i. 5a + 2b ii. |3a -…

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Q: What is the derivative of y = √5x² + 3x + 2 where x = 1? O no correct answer O2.054 O 2.057 O2.056 O…

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Q: Find the critical numbers of the function 2x5 – 5x¹ – 10x³ – 4 and classify them using a = f(x)…

A: We need to find critical numbers and classify them.

Q: 12 [ sin* ‡nxdx

A: We can find the answer as below

Q: C. length x, width = D. length = 2x, width - [Select] da = 24 = 24 V What is the appropriate…

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Q: If f(x) = 5x(sin x + cos x), what is f'(x)? O 5 (sin(x) + cos(x)) -5x (cos(x) - sin(x)) No correct…

A: Derivative of product: ddxuv=udvdx+vdudx

Q: Question x² Find the lower sum for f(x) = 5- on the interval [1, 5] using 4 rectangles. 5 10 F…

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Q: 12. dx Ve -1

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Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Consider the differential equation y 4xy (In y)² Find the solution that passes through the point (0,…

A: The given data is: y'=4xy(lny)2  To find the solution that passes through the point (0,e)

Q: The fox population in a certain region has a continuous growth rate of 4 percent per year. It is…

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Q: If 10 fro A True B) False f(x) dx = 17 and 8 Lof(x) d f(x) dx = 12, then 10 ["fo f(x) dx=5

A: ∫010 f(x)dx = 17 ∫08 f(x)dx = 12 ∫810 f(x)dx = 5

Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: Given

Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: On solving this we will get

Q: 17. √16-e² -dx

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Q: figure out absolute min & max values: g(x)=cos^2(x)-3sin(x) Interval:0<=x<=pi

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Q: x² +11x+30 4x+20 For items 37-38: Given the function f(x) = [Select] 37. What is f' (6)? [Select]…

A: Given  f(x) = x2 +11x+304x +20    ------(1)

Q: La te is 6x⁹-x5+ 4 A T B 2n C) None Л D 2 E) 0 dx is equal to

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Q: What is the derivative of y = (4x2 + 9x + 1)e-2? O no correct answer Oye-2 [2(4x² + 9x + 1) + (8x…

A: Solve the following

Q: Which of the following is a point on the plane with equation n = (-3, -2, 2) + t(2, 2, -2) + s(1,…

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Q: 1. Find the inverse of 3x + 1 = 4. x-1 (1) y = x (2) x = y-1 10 (3) x = 3y + 1 (4) y = x+1

A: Given :3x+1=ythenf(x)=y=3x+1

Q: 5x Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-₁ 4 (A) 3.667…

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Q: Given the function f(x) = 5x(sin x + cosa) what is f' (4)? O No correct answer O -1.996 O -2.99 Ⓒ…

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Q: Directions: Find the area of the region bounded by the curves. Use a clean sheet of paper for your…

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Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: Find v. v=-4i-j ||v||=| (Simplify your answer. Type an exact answer, using radicals as needed.)

A: Here, the given vector is: v=-4i-j=(-4)+(-1)j

Q: 4. f sin3x sin2xdx =

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Q: Find equations for the tangent line and normal line to the circle at each given point. (The normal…

A: The circle equation x2+y2=25

Q: Find if x-t³+1 and y=4t²-4t. d²y dx²

A: Solution of given question is written in below steps.

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: Timothy heard that he could triple his money in 27 years if he invested it in his friend's business.…

A: To find the compound interest.

Q: 5 dx Evaluate: (x-3)² 1 A B C D E -1 ∞o (does not exist) 1 0 None

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Q: The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has the…

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

A: Given:a=-3i+2jb=2i+aj

Q: Find the length of curve x = t², y = t³ from x = 0 to x = 5.

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Q: S (x - 8)dx x (x + 5)²

A: see below the answer and calculation

Q: 1 f(x) = (2x³ + 6) ³

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Q: Suppose y = sina, which is TRUE about y? 1 Oy= sin O none of the above y 0 *= arcsing O * = sin y

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Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: The given problem is solved below in detail.