Differential Operator General Solution DN AxN-1 + BxN-2 +..+C (D - a)N AxN-leax + BxN-2eax + ... (D? + B?) A cos(Bx) + Bsin(Bx) Given the differential equation y" + 16y = 5 x³ The combined set of Differential Operators for this differential equation is D4 (D² + 16) Find the General Solution for the differential equation. (A y(x) = Ax³ + Bx? + Cx + D + Ee-16x + Fe-16r B y(x) = Ax + Bx3 + Cx2 + Dx + E + Fcos(4x) + Gsin(4x) y(x) = Ax4 + Bcos(4x) + Csin(4x) (D y(x) = Ax3 + Bcos(4x) + Csin(4x) E y(x) = A x³e-4 + Bxe-4 F y(x) = Ax³ + Bx? + Cx + D + Ecos(4x) + Fsin(4x)

Q: y = (x' - 2x2 +3) (7x² – 4x)

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Q: Find a parameterization for each of the following surfaces: (a) æ² + y² + z² – 4x – 6y = 12 (b) 2x² ...

A: We have to find the parametric representation of the following surfaces: x2+y2+z2-4x-6y=12       → ...

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.) [(3cos...

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: V(x) = In(sin(x) – cot(x))

A: Use the formula of derivative of composition of functions

Q: 2. Summation of a constant: E,=c, +c, +c3 +...+ c, = nc %3D Example Evaluate the following summation...

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Q: An ellipsoid S has the parametric equation S (0, Ø) = (cos0 sing, 2sino sinø, 4cos ø) where 0 and øa...

A: Given equation of ellipsoid S(θ,ϕ)=cosθ sinϕ , 2 sinθ sinϕ , 4 cosϕ

Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x² + 10. ...

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Q: Find all the local maxima, local minima, and saddle points of the given function. f(x.y) = x? + xy +...

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Q: 20. Find the equation of the curve for which y" = x, and which passes through the point (1, 2) and t...

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis...

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Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin...

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Q: Write an equation for a cost function where the fixed costs are $2300 and the variable costs are $20...

A: Given data: Fixed cost= F= $2300 Variable cost=V= $20

Q: Which of the following statement/s is/are true about the function whose graph is shown below? A. lim...

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Q: 3cos3x-1 uate f dx, the integrand can be tran 1-sin2x Bcos3x + csc²x)dx

A: We have to choose the correct answer from the given options according to the given information

Q: (2xy-tany)dx + (x² – xsec*y)dy = 0; y(1) = *

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Q: Question 4 of 10 2 -10-8 -6 -4 -2 2. 4. 6. 10 -6 -10 y 10 4 -10 -8 -6 -4 -2 2 4 6 8 10 -6 -8 10 y 1...

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Q: 4. Determine if the relations given by the graphs below give y as a function of x. If so, determine ...

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Q: 47. For the equation: y= Vx? + 20x dy ay using the chain rule dx a. Find а. b. Find the slope of the...

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Q: A central angle ? in a circle of radius 7 m is subtended by an arc of length 8 m. Find the measure o...

A: we have to determine degree 

Q: Forms of Summation Notation 5. Sum of the squares of the variables: Ex = x,² +x,' +..+x,² i=1 Exampl...

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Q: If labor (x) costs $235 per unit, materials (y) cost $169 per unit, and capital (z) costs $60 per un...

A: Given that: Labour costs $235 per unitMaterials y cost $169 per unitCapital z costs $60 per unit.

Q: Given the following non-homogeneous system of first-order linear differential equation: v = 5 y, + 3...

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Q: 17. Find the area enclosed by the x-axis and the curve y = -x² +9 32 s.u. а. 3 b. 18 s.u. с. 36 s.u....

A: Find the area enclosed by the x-axis and the curve y= -x2+9 

Q: What is the equation (mathematical expression) for a hollow sphere with center at the origin and rad...

A: According to question,Given,Center of hollow sphere =Origin 0,0,0,Radius = 10

Q: Second-order non-homogeneous ordinary differential equation given a y" +3y' – 10y = e²* Calculate th...

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Q: In Problems 59-66, use the price-demand equation to find the values of p for which demand is elastic...

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Q: Question 1 If f(x)dx = 5, Lf(x)dx = 2, and fi f(x) dx = -1, find f(x)dx. ... А.) —2 В.) 2 С.) —3 D.)...

A: ∫ab f(x) dx =-∫ba f(x) dx ∫ab f(x) dx = ∫ac f(x) dx +∫cb f(x) dx

Q: I. Determine the Fourier series of the following J sin(t) (0 <t<T) (7<I<2x) f(t) = a. Half-wave reci...

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Q: 5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) = -12(cos3t)csc(si...

A: Topic = Derivative

Q: x = 2. What is the value of y when x = -1? а. —3 b. 3 15 С. d. 3

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Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

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Q: ssume you are given the surface S with equation æ² + + = 1. = 1. 9

A: We can use distance formula to solve the problem

Q: Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero betw...

A: Given function,f(x)=9x3+10x+6 between -1 and 0Therefore ,f(-1)=9(-1)3+10(-1)+6f(-1)=9(-1)-10+6f(-1)=...

Q: Test the series below for convergence using the ratio test. n+ 2 24n +1 n=1 The limit of the ratio t...

A: Given: ∑n=1∞ n+224n+1where f(n)= n+224n+1Ratio test : l=limn→∞ an+1anif l&lt;1 then the series is co...

Q: 2. Find the indicated values. f(g(3)) f(x) 9(x) 51 54 S(8(1)) g(S(1)) 4- 4- 8(5(0)) 3 S(S(5)) 2- 2 S...

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Q: 13. S S(x)dx = 5, f(x)dx = 2, and f f(x) dx = -1, find f(x)dx. If %3D а. —2 b. 2 С. —3 d. 3

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Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Use energy conservation equation.

Q: Given a function whose graph is shown below 6- 5- 4- f(x) -3 -2 |-i 0 1 2 3 4 5 -1 -3 What is f(1)? ...

A: for x=1 there is no corresponding y value , That is there is no close circle for x=1, Therefore f(1)...

Q: 6. If f(x)dx = 5, f f)dx =2, and , f(x) dx = –1, find i f)dx. а. —2 b. 2 C. -3 d. 3

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Q: Sketch a possible graph of a function that satisfies the given conditions. f(-1) = -7; lim f(x) = -2...

A: Given that f(-1) = -7. Therefore (-1,7) is a point on the graph .when x tends to -1 from the left si...

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: 18( cos54 + isin54°) 3(cos102" + isin102" )

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Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3 c...

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Q: (x² +3y² +5)dx +(6xy+ 6y+3)dy = 0 Identify the exactness of the differential equation. Calculate the...

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Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin ...

A: We will find the anti derivative. 

Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y= 2x–y dx

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Q: Calculate the difference quotient for f (x) = 5- x² at a = 3. (Express numbers in exact form. Use sy...

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Q: Find a (real) general solution. y" + 2y' + 2y = 4e¯* sec³x

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Q: The limit represents a derivative f' (a). Determine f (x) and a. 6h lim h 1 h-0 (Express numbers in ...

A: find fx and alimh→06h-1h