3. y'-5y =xe* –xe"

Q: Consider the function T = xe3x+y? dy 5 and dt where x = Vt + 1, and when t O we have y -2. dT when t...

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Q: Radium decomposes at a rate proportional to the amount present at any instant. If initially there w...

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Q: A. f (t) = So sin(t - T) cos(7)dT

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Q: Find the Maclaurin series for the function f(x) = ln(3 + 4x)

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0       fx=f0+f'01!x+f''02!x...

Q: 3x2 + 6, x 0 1+ 9x + x3' Find the following limits. NOTE: Enter an exact limit if it exists. If the ...

A: This question is based on Limits.

Q: Consider the function f(х, у) — у4г — Зу. /Ах — Зу. - a) Find all second order partial derivatives o...

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Q: a. 15. A committee of three is to be formed from a group of four Math teachers and five Science teac...

A: topic - permutations and combinations

Q: having

A: We will find the half life. 

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

A: The given series,       ∑k=1∞-1011k-1

Q: 9. An employee borrows Php60,000 for seven months at an interest rate of 12% per year. Find the inte...

A: Principal=P=Php60,000 Rate=r=12% per year Time=t=7 months=712 years Interest=Int=P×r×t100=60000×12×7...

Q: 3. lim cos X

A: Given: limx→0cos(x)   We know that; cos-θ=cosθ   Let, fx=cosx

Q: Determine the domain of f(x, y) = In (x² – y) %3D А. On and above the parabola y = a. В. On and belo...

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Q: WHich of the following represents the shell height if the shell method will be used to find the volu...

A: Given problem:- Which of the following represents the shell height if the shell method will be used ...

Q: Find the area bounded by the indicated equations. y = x 5, x = -5, x = 1, y = 0 В) 2604 15625 6 7813...

A: Given: y=x5, x=-5, x=1, y=0 The area of the curve by the bounded region is given by: A=∫x5dx Here, t...

Q: An+1 Use the ratio to determine if the sequence { ne" }, +o is strictly increasing or strictly decre...

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Q: Write the first five terms of the sequence: 13 In n n n=1 Determine whether the sequence converges, ...

A: To find out the first five terms of the sequence and also find out its limit if it is converging or ...

Q: Eliminate the arbitrary constant y2 = C1x2 + C2x

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Q: Evaluate the following integrals. sin" r 0. cos a kle

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Q: 1 eB*[Scos2x - psin2x] + C *sin2xdx a Find: a + B + 8 + p

A: The given integral is e-3xsin(2x).

Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+7z=46. Roun...

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Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

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Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³+81=0 B ® [1+(y")*]³–81=o [1+(y')²]³– ...

A: The general equation of the circle with center (h,k) and radius r is             ( x - h )2 + ( y - ...

Q: Evaluate the integral. dx 3x2 + 11x + 6 0.

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Q: = Homework: HW10--3.1 a. For the function and point below, find f'(a). b. Determine an equation of t...

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Q: . Find all the second-order partial derivatives of the function z = f(x, y) = e2xe"

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Q: 1 Eliminabe the arbitrary constants C,e"cos 2x - 3X SIn 2x + - ZX Y C,e

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Q: Use the difference an+1 - an to show that the given sequence {a, } is strictly increasing or strictl...

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x3 – 3x? + 4x – 12

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other que...

Q: (sim (6)) 45. y - (1 + uan ()) 6. y = ¿(1 + cos (7)" 43. y sin (cos (2r - 5)) Eises 44. y= cos (5 si...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: Consider the following sequence: {an} = {n – n² },=-1 Use an+1 - an to show that the given sequence ...

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Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your...

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the constan...

Q: 2. Which is the interpretation of the statement lim f(x) = L ? i. For all x values close to c, but n...

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Q: Assume that functions f and g are differentiable with f(- 3) = 4, f'(- 3) = - 4, g(- 3) = - 4, and g...

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Q: Express the repeating decimal as a fraction. 0.2513 23 23 23..

A: We can express the given repeating decimal as fraction as below.

Q: 6. x sec x tan x dx

A: Let's find. 

Q: Find r'(t)⋅r''(t)forr(t)=−3t^5i+5tj+2t^2k

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Q: Given the function: f(x, y) = y°e -5x a. Find fyy(x, y) b. Find fyyæz (0, 1)

A: a)f(x,y)=y3e-5xPartial differetiate w.r.t yfy(x,y)=3y2e-5xPartial differetiate w.r.t yfyy(x,y)=6ye-5...

Q: If f(x)dx=cot x² +C , then f (x) is equal to A -2cscx? B -2xcsc?x? © In/cscx²| D O In/sinx²|

A: We have to choose correct option for value of f(x)

Q: Find the general solution of y"- 10y'+ 25y - 0 Oy= Ce- + C2ze* Oy - Ce + Cwela Oy- Ce a + C,ze be Oy...

A: Given,y'' -10 y' + 25y = 0     .......1this is homogeneous equation.Since,y" = D2yy'=DySo putting in...

Q: Write the first five terms of the sequence: 13 In n n n=1 Determine whether the sequence converges, ...

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Q: |(1+ sin x)'cos x in x) cos x cOS.

A: Given: ∫1+sinx3cosxdx

Q: Solve the differential equation (xy – 6x²)dy – (2y² – 9xy)dx when x = 1, y = 1

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Q: Question 1 If T is a linear transformation such that T(1, 0, 0) = 2, T(0, 1, 0) = 3, and T(0, 0, 1) ...

A: A detailed solution given below.

Q: (c) Determine if F is a conservative vector field. Given that the charged particle is moving along t...

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Q: What is the magnitude of the resultant of the two force vectors shown in the diagram? (-2,3) 3- 2- (...

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Q: Determine the Laplace Transform of the given integral equation. A. f (t) = S sin(t - 7) cos(7)dr

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Q: Find the Maclaurin Series for the function f(x) = sinx

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+6z=33. Roun...

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use ...

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Q: 20. Let h be the function defined by h(x) : L, sin²t dt. Which of the following is an equation for t...

A: First we find h(x) , using 2sin2x=1-cos2x Then equation of tangent is y-y0 =m(x-x0 )