Solve the given IVP using Laplace Transforms. Solve for x(s) and STOP! (Express x(s) as a single fraction.) x" + 9x cos(3t), x(0)=0, x'(0) = 2

Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: T Find the net area and the area of the region bounded by y = 2 cos x and the x-axis between x = -…

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Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

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Q: 2) Since the series can be rewritten in the form a = r= k-1 "§ ²³ (4) ². k=1 Give exact answers (in…

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Q: رح 3 2 + + + + 32 - 2 -3x+2) 22م dx

A: I have stated the used formulas in the solution

Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

Q: Convert the rectangular coordinates to polar form (√8,√8) (4,57) (√2,73) Option 4 O Option 1 (2,3)…

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Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: Write a recursive formula for the arithmetic sequence an given below. an= and a1= 10,19,28,37,46,…

A: To write a recursive formula for the arithmetic sequence given below.an=? and a1=?10, 19, 28, 37,…

Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: 6 Find an equation of the line to the curve Y= √x that is parallel to the line 6x +Y=1. Y =

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Q: Let f be a function given in the graph below. Note that the domain of f is [-3, 4]. a) Does f have…

A: Given the graph of a function. To determine whether the function has an inverse on the given…

Q: Use identities to find values of the sine and cosine functions of the function for the angle…

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Q: If a = (-1,-4, 4) and b =, then a × b equals: O-4i-k O 4i + k O i +4k O 4i+k None of the others.

A: We can find the cross product as below.

Q: ST ry² ds where C' is the right half of the circle x² + y² = 9 Evaluate

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = 3x…

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Q: Q2: Solve the following first-order differential equation x.e +y.- = 0 for y(0) = 1; x = 0. dx (2)…

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Q: Find a linear differential equation with constant coefficients satisfied by e2x, e-x, e3x and e6x

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: (,1) Convert (5,5) to rectangular coordinates: (solve) Option 2 Option 3 (3√5,2) Option 4 Option 1…

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Q: Find the amplitude, period, and phase shift of the function. =I 1 sin (3x-x)+3 Give the exact…

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Q: Find the absolute maximum of f(x) = x3 −6x2 + 12x + 3 on [0,3]

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Q: z=(4xy)/[(x^2)+(y^2)] (a) (partialz)/(partialx)

A: We have to find the partial derivative.

Q: a 3. Sketch the graph of +₁ f(₂)=1₁ continous function & $²(2)=0, the point (2,1) is 2 £ is…

A: Let's solve.

Q: Problem 2. Find the area between these curves: (a) f(x) = 5x-2 and g(x) = 4x + 1 on the interval…

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: x4 dx X³- 2x²-7X-4

A: The given integral is: I=∫x4x3-2x2-7x-4dx   As we know the common integral.…

Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

A: We have to solve above differential equations

Q: Solve the equation. dx dt 2xt² C An implicit solution in the form F(t,x) = C is =C, where C is an…

A: To find the solution of given differential equation.

Q: This is the approximate time right ? Making the no. of days from feb to aug into 30, by that logic…

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Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: answer is in next step.

Q: 16. A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x)…

A: We need to find P(x).

Q: 1₁ f(x)dx = 6 ln([x]) - 6 ln(|x]) — -—-cos(5x). -cos(5x) - 3e + x² + 6x + C

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Q: dz 10. Evaluate the integral where C is a simple closed curve cz(z - 1)' in the positive direction…

A: The integral ∫Cdzzz-1, where C is the simple closed curve in the positive directionthat contains the…

Q: In a pool filled with water to a depth of 1 Rectangular plate calculate the fluid force on one side…

A: Given: Depth of pool = 10ft Area of rectangular plate, A = 3ft×4ft=12 ft2  Hydrostatic Force on…

Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: Match the equation with its graph. r(t) = cos(nt)i + sin(лt)j + t²k, Need Help? + 2 Z -2 Read It N₂…

A: Given problem:- r(t)=cos(πt)i+sin(πt)j+t2k  To find:- Draw the graph of given curve

Q: Problem 2 Solve y" - 25 y = x ex

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Q: Given the curves y=(x^2)/2​  −4·x and y=−x^2+8,   Sketch both curves on the same coordinate plane…

A: Let's solve.

Q: ydy 2 √16-94² S

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Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: A 2x-In Ixl+C B 2x4 In Ixl+C 5*²=4 dx x D HIN x² - In Ixl+C x² - 4 In 1x1+C

A: topic- indefinite integral ∫xndx=xn+1n+1+C∫1xdx=lnx+C

Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(v2). -x²z sin(yz)…

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Q: Use the derivative f'(x) = x²(x - 5)(x + 5) to determine the local maxima and minima of f and the…

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Q: if f(x,y) = √x² + y + 4, then find a a21 and ах ду х

A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: For the function f(x)= (8+2x, if x5) A) use definition of continuity at a number (3- step test) B)…

A: Concept: These are the three requirements for continuity: 1). The equation for the function is x =…

Q: S cos 2x dx COSX

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Q: Evaluate the ff (show all steps) dx (4-x²) 3/2 √

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Q: Find u-v, 2(u + 3v), and 2v-u. u-(6, 0, -5, 8), v= (0, 4, 8, 6) u-v (b) 2(u + 3v) - (c) 2v-u-

A: To find out u-v, 2(u+3v), 2v-u

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. 32 y = 9x, x…

A: Given that Y= 9x - 32/x ; x= 4. And we find curvature and curvature of the plane at give x value.…