Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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Q: lim x→5 3x |x-5|

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Q: By power Series method, Solve the following ODES • (2+x)y=y ans: y = a. (1+1=1/2 X

A: In this question we have to find the solution of the power series.

Q: Find f(x+h)-f(x)/h for the given function . f(x)=x2+8x

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Q: 10. 2ste tds +(s²e-t - t)dt = 0

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Q: 1 For the parametric curve * = find an equation for the tangent line to the curve at the point…

A: To find equation of tangent line:

Q: The graph below is the function f(x) t lim →-3 lim I-3+ lim 5+ 4 → 3 N WA -3 -2 -1 -1 3 2 Find the…

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Q: 106) Iff"(x) and (c,f(c)) is the point lying on the curve for which F(c) is maximum, then f'(c) is…

A: If f''x<0 ∀ x∈a,b and c is a point such that a<c<b, and c,fc is the point lying on the…

Q: 3 Solve the following ODES by Inverse Operator method 2 • (B³² +1) y = cos x 11

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Q: 3. Apply the Integral Test to show whether or not the series converges. You do not have to show the…

A: We have to find the convergence test

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: Solve for t, 0 < t < 2π 14 sin(t)cos (t) = 8 sin(t) t = 0.96,5.32 Give your answers accurate to at…

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Q: Use the binomial series (x + 1)k = 1+ kx + for x < 1 to approximate (² Xx k(k − 1) 2! X- + k(k −…

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Q: Solve the problem. 16) The graph shows the height h (in meters) of a roller coaster t seconds after…

A: In this question, we need to find the time intervals in which the height of roller caster is…

Q: el For the function z = f(x,y) = - 4x³ -6y² - 7xy, find t V ne ON dz dx dz 3x forr || f(-5,4)=…

A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

Q: Find the composite functions (f. g) and (gf). What is the domain of each composite function?…

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Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the…

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Q: A textbook company publishes computer, educational and utility type of books. Their business…

A: We have to find how many educational books should the company publish annually for maximum profit.

Q: 1. [cos³x dx [Use the reduction formula]

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Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: z²i+xzj+ye² of the sphere x² + y² + z² Given F = 2 [[ S 50 that lies inside the cone z = √x² + y²…

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Q: 2 (D² +8D³² +16) y = - sinx Ans: Y = C₁ cus2x+ C₂ Sin2x + C3 Xcos2x + C4 X sinex-_-_sing

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

Q: PLEASE

A: As per policy only first question is answered. Please refer to the image below

Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: Find f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: Find the Laplace Transform of f(t) = te cos(3t) (A) B D s+1 s² (s+ 1)² +9s² = ((5+1) ²+9) S s²…

A: This question is related to Laplace transform, we will solve it using given information.

Q: -y(2x+y) x(x+2y) - y'=-

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Find the absolute extreme values of the function on the interval. F(x)= == 3 21 0.5≤x≤2 OA. absolute…

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Q: Find the Laplace Transform of f(t) = 3e + 4t² - 2

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = x4 –…

A: Here is the solution:

Q: Solve the differential equation by variation of parameters. 1 8 + ex y" + 3y + 2y =

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Q: Using Desmos or other graphing software, sketch the graph of y = sin (2x). a. Using the tangents,…

A: Y=sin(2x)

Q: 5. An object has a constant acceleration of 10 ft/sec², an initial velocity of -20 ft/sec, and an…

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Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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Q: 5. It was noon on a cold December day in Tampa: 16°C. Detective Taylor arrived at the crime scene to…

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Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: (a) Find x, y, z and B, where Tox 37 A = 1 -3 y A² = 1; C(4+1)+3B7 = 2A, and I: unit matrix ; 4 o…

A: Please re-state the subpart (b) properly.   To find the values of x, y, z and the matrix B=?

Q: 8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

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Q: Зу" +y=0.

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Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: Consider a pool shaped like the bottom half of a sphere, being filled at a rate of 25ft^3/min.the…

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Q: 2 Solve the following ODES by Inverse Operator method. 1.2 y - 2y +y = e sinx "LI X Xx Ans:…

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Q: A box without a lid is required to have volume, V = 32000 cm^3. Minimize the amount of cardboard…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: For a certain automobile, M(x) = - .015x² +1.32x-7.3, 30≤x≤ 60, represents the miles per gallon…

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Q: n=1 [cos-²x dx] n 2. Derive the reduction formula for cos"x. [fcos"x dx= cos x sinxn- n

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Q: 2. Set up, but do not evaluate, the integral which gives the volume when the region bounded by the…

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Q: Using the circular disk method, find the volume of the solid generated by revolving about the…

A: Given curves , y=x ,                   (1)x=4.                       (2)