Find the solution of the following differential equations. Show your solutions 6. (D6 + 3D + 3D² + 1) = 0

Q: An rectangular metal box without a top is to be made with panels that are 0.5 inch thick. The inside…

A: let b = width l = length h = height Given each panel has 0.5 inch thicknessso db = dl = dh = 0.5 in

Q: 8. Find the slope of the tangent line to polar curve r=1+2 cos 0 at 0 = π/3.

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Q: 3x ſ¹ S³* S*** ( 3x + 4y − 5z) dy dz dx - -2x x-z

A: The given integral is  ∫01∫-2x3x∫x-zx+z3x+4y-5zdy dz dx

Q: Use the fact that ∞ 2 sin x cos x = n=0 ∞ to find the power series expansion of sin² x at x = 0. n=0…

A: Given the fact that 2sinxcosx=∑n=0∞-1n2nx2n+12n+1!.It is required to find the power series expansion…

Q: Given the function f(x) = - x2 - 4x - 3 a) What is the maximum value of the function? Why? b) What…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: dw For the given functions, (a) express t as a function of t, both by using the chain rule and by…

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Q: An arithmetic sequence has a15 = 86 and a34 = 200. Find a150. an = a₁ + (n − 1)d -

A: NOTE: Refresh your page if you can't see any equations. . it is given that

Q: Find the x-values of all points where the function has any relative extrema. Find the value(s) of…

A: Let's find relative extrema.

Q: Consider the following curve. ² = sin(28) Ф. Set up an integral that can be used to find the shaded…

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Q: Where on the interval [0, 7] is the secant line parallel to the tangent line for y = x sinx?

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Q: Given f(x) = -(2x - 1)2 (4 + 3x) a) What are the x and y intercepts? b) Determine the end…

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Q: Find the volume of a soild generated by roatating the region bounded by f(x)= x^3 and g(x)=2-x^2 and…

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Q: If the function y = 2x² is integrated between the limits of x = - 3 and x = + 3, the result is ____

A: The function is given by y = 2x2 To evaluate: The integration of the function between the limits…

Q: Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

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Q: ind the Maclaurin Series for f(x) =1/(1+8x) and its interval of convergence.

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Q: The function g is defined as follows. g(x)= (a) = Find the following limits. If a limit does not…

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Q: Find the limit algebraically. lim h→0 (f(-2+h)-f(-2)) h where f(x) = -4x²-x+1

A: Given function:- fx=-4x2-x+1

Q: Find the total differential. dw = w = eбy cos(4x) + z10

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Q: 12 Find the work done for a force F = N from x =1 to x =6 m. x²

A: Given: Force F=12x2 from x=1 to x=6 m

Q: Convert the following equation to polar coordinates. y=7x² F

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Q: Find the present value of an ordinary annuity with deposits of $11,788 each year for 9 years at 6.0%…

A: Topic = Algebra

Q: Find the velocity and acceleration vectors in terms of u, and up. do r = a cos 40 and dt V= = 4t,…

A: Solution Given r= acos(4theta)

Q: Find the degree three Taylor polynomial T3 centered at x = 0 for f when f(x)= = 1 (4x + 1)¹/2 1.…

A: Given that , fx=14x+112 find the degree three Taylor polynomial centered at x=0.

Q: 1. 2. 3. Let f(x)=-=-2 Find and simplify/(x+h)-f(x) h Let f(x)=√x-2. Find and simplify f(x+h)-f(x) h…

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Q: Evaluate the integral. π/2 x/2 1 [co 0 [cos 9ti-2 sin tj+ sin² 5t k] dt [cos 9ti-2 sin tj+ sin² 5t…

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Q: Given sinx: 161 289 225 289 161 289 225 289 15 and cos x > 0, what is the exact solution of cos 2x?…

A: Givensinx=-1517 and cosx>0 We are required to find the exact solution of  cos2x

Q: The topic is linear differential equation, answer should have the equation and the general solution

A: Please seethe below answer.

Q: Find the inverse of the function. y = 5x +7 A) y= log5 (x-7) B) y= log6-2x C) y= log22x D) y =…

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Q: Find the equation of the plane tangent to the surface G(x, y, z) = 3x² - y² - 2x² = −14 at P = (1,…

A: G(x,y,z)=3x2-y2-2z2  given pointis  (1,-3,2)equation of plane in standard form is…

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A: given  F''(x)=Ax+BF'(1)=r and  F(1)=sF'(x)=∫(Ax+B)dx∫xndx=xn+1n+1+c

Q: If yo is the solution of the equations xy' + 3y = 2x, y(1) = 8, determine the value of yo(2).

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Q: (E) What is the form of the general solution to this differential equation?

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Q: dy dx - y = ex ; y(0) = −2

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

Q: Exercise 1.1: Apply integration by parts once to get 2n In(a) = [(1 - 2²)" cos(az)dz = ²"…

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Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

A: (a).   Given                          F⇀ (x,y) =(4x,4y)         {vector field}Compute the…

Q: 2. tds = (3t+1)s dt + t³e³t dt

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Q: Find the value(s) of ß for which y (t) = cos(ßt) satisfies y” + 100y = 0

A: Given that yt=cosβt satisfies the equation y''+100y=0. We have to find the values of β.

Q: Which of the following can cos² be simplified to? 0 1-sin O 1 + sin e 01 - sin e O sin e O cos -…

A: Given expression: cos2θ1-sinθ

Q: Evaluate the following integral ffe D es da over the given region D, where D = {(x,y)|1 ≤ y ≤7,0 < x…

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Q: Pizza House offers 2 different salads, 3 different kinds of pizza, and 4 different desserts. How…

A: Please see the below picture for detailed solution.

Q: B. Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

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Q: R = √√√6

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Q: C. Evaluate the following inverse Laplace transforms. 3 1. C-1 (125 + -1 (125 + (+52) (s+5)²)

A: L-1{ 125s6 + 3( s + 5 )2 } Formula used L-1{ 1sn } = tn-1( n - 1 )!L{ e-atf( t ) } = F( s + a )L-1{…

Q: Find f'(-2) if f(x) = 3 X 8 - 9x.

A: Given,           fx=x38-9xTo find : Find f'-2

Q: (1) Find the radius and the interval of convergence of the power series. Be sure to check the…

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Q: 2x-5 dx x²-2x-8

A: To solve the following problem of Integration

Q: Find the following limits for f (x) lim f(x) = 0 x-4 If necessary, select the most informative…

A: Given query is to find indicated limit.

Q: Problem 3:Linear Equation xdy - 2ydx = (x - 2)e* dx

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Q: Suppose that A. B. 0.5 food f(2t) dt = = 0.125 0.5 [ f(t) dt = 11. Calculate each of the following.…

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