Find a formula for the sum of n terms. Use the formula to find the limit as n Ilm (-1)²

Q: Let f(x) = 2log₁(x) f'(x)= ƒ' (6) =

A: We have to solve above question

Q: Devin invested an amount of $10,000.00 in a mutual fund. After 2 years and 6 months the accumulated…

A: The solution is given below

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given: ∫05|10x-5|dx

Q: 60° IIPII=23 Q Find the EXACT components of the vector above using the angle shown. P Check Answer…

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Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

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Q: Evaluate £¹₁7 x8 − 7 x³ + 7 x² dx. Round your answer to two decimal places. £²₁7 r8 − 7 x³ +7 r² dr…

A: Given definite integral is: ∫-11(7x8-7x3+7x2) dx

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 5t, where 0 ≤ t ≤ 1.5…

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Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

Q: Vincent purchased a car using a 5-year car lease at 4.50% compounded quarterly that required her to…

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Q: f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x)…

A: The given limit is limx→∞fxgx=0

Q: Exercises: Use the theorems on limits to evaluate each of the following, if it exists. 1. lim (2x³…

A: See this solution in below.

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

A: The region R is enclosed between the curves x2=y-1 and y=5 we have to sketch the region R and find…

Q: , b) Find the angle ZB.

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Q: Find the domain and range of the function.   ​G(t​)=1/t2-25

A: Given,            Gt=1t2-25To find : Find the domain and range of the function.

Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

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Q: Assume that the shape of the athlete's high-jump is parabolic. the function, in vertex form, where…

A: The axis of symmetry is t = 0.6 and the maximum height is 1.80 mhence the vertex is  (0.6, 1.80)

Q: A tank half-filled with water is in the form of a rectangular parallel piped 5ft deep, 15 ft wide…

A: Answer is c

Q: Z= (a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0, 0,…

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Q: Find 2 -1 (3x³ + 7x¹) dx

A: Here we have to solve definite integral

Q: Write a limit using summations that would equal So 0 tan (2x) dx.

A: The integral is given by ∫01tan2xdx To evaluate: The limit using summation that is equal to the…

Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

Q: Consider the following function. f(x) = (x-8)e* (a) Find the critical numbers of f. (Enter your…

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Q: Find two positive numbers with product 625 and whose sum is a minimum. Enter your answers in…

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Q: 0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the…

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Q: 4. The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line…

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Q: Given f''(x) = 7x - 2 and f'(0) 2 and f(0) = 1. Find f'(x): and find f(4) =

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Q: 3. a. Solve the differential equation y'= 2x√/1-y² b. Explain why the initial value problem y'=…

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Q: TU 2. fz sin² x cos4 x dx J

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Q: 37. Problem Using polar coordinates, a point is at (7, 38). Find its rectangular coordinates. a)…

A: As per bertleby guideline I  have to solve only problem 37. For answer to others resubmit the…

Q: J 9(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 9², x ≥ 0, y ≥ 0,0 ≤ z ≤ 4} and g(x, y, z)…

A: Please see the below picture for detailed solution.

Q: 1 6. √₁² √ 1 - √u du

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Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

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Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

A: Centerville is located at 10,0 in the xy-plane Springfield is at 0,5 Shelbyville is at 0,-5 The…

Q: This is all one question. I really need help on this. Thank you so much

A: Given: peter goes on a ferris wheel that has a diameter of 36 feet and the distance fro the bottom…

Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

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Q: Solve (2y³ – x³) dx + 3xy² dy=0; y (1) = 1 O a. x² (5y³ x ³) = 4 b. ? (5y® — g - 23) x³) = 0 ○ c. x²…

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Q: i) lim cos x-0 7 πCOS²x x²

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Q: Evaluate J 2xz dV where E = E Round your answer to four decimal places. {(x, y, z) | 2 ≤ x ≤ 5, x ≤…

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Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

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Q: 2. A force F = [-2,1,5] in Newtons, pulls a sled through a displacement s = [-3, 5, 4] in metres.…

A: Using dot product of vectors and obtain the magnitude of the force vector

Q: 3x³-28x² +40x-42 3x² - 4x+5 dx

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Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

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Q: Find the work required to move an object in the force field F = (x,2) along the straight line from…

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Q: Let v = 37 - 47 + 2k. Find ||||. Check Answer

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