5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under Prove your answer with your solution. A. Case 1: Distinct Real Roots B. Case 2: Repeated Real Roots C. Case 3: Distinct Imaginary Roots D. Case 4: Repeated Imaginary Roots 6. Which of the following is the general solution of the differential equation in number 5? A. y = cxe3* +cze3x B. y = ₁е-²x + c₂e²x + c₂e²x C. y= cxe2* +Czxe-2x D. y= cx3e-2x + 2xze-2x

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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A: We need to evaluate the value of the following limit limx→12-x-xx-1

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Q: Solve the following y" - 3y' + 2y = 2x2 + ex + 2xex + 4e3x -

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Q: S₁² = P² 1 хо A (-∞,1] B {0,1} с (1,00) D (-∞0,00) Given dx, determine all value/values of P for…

A: Here we have to determine all values of p in which the given improper integral is converges.

Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

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Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: MEAN VALUE THEOREM Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given…

A: Mean value theorem is valid.

Q: Using the method of variation of parameters, the form of a particular solution pof (D²+25)y=4x²-3e5x…

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Q: The function is z = Determine ე3 2 əyəwəx wx²y + xy² + tan (wx)

A: A detailed solution is given below.

Q: C) (-∞,1]

A:

Q: 7. Find the area bounded by the parabolas x² - 4y = = using vertical strip. 0 0 and x² + 2y and x² +…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A) none B) 1 infinitely…

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Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: 2. Find the area under the curve y = x² from x = 0 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

A: Solved below.

Q: y = 2 sin 3x 1+3cos2x

A: We can solve this as follows:

Q: A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward…

Q: Given A B U D ₁₁f(x) dx = 0 and 0 1 f²³f(x) 11 6 11 55 6 f(x) dx = 11 6 * evaluate ,0 √3f(x) dx -…

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Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

Q: The reverse order of fo Say હરે e² dxdy is equal to e-1 8e None of them

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Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: Find the absolute maximum and minimum values of the function, subject to the given constraints.…

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 A 2-unit² 1 Ⓡ / unit²…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: 4. Use the washer method to determine the volume of the solid obtained by the revolving the region…

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Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A: A critical point is a point where the derivative of the function is 0 or does not exist. At critical…

Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

Q: The improper integral +∞ [+00 0 ex dx is

A: Our Aim is to evaluate the improper integral given below:-∫0∞e-x dx -(i)

Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D^3 – 2D + 4)y = 0 ; y = –2 , Dy = 8, D^2y = 0, when x =…

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Q: Solve the integral: Seln(2x² + 3x-4)³ (4x + 3) dx eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) A + C…

A: We know eln(x) =x

Q: Solve x² = 4y + 4 and x = y = 2 128 A sq. units 5 B none of the choices 2 21 sq. units 3 for the…

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Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: 3. The auxiliary equation of the differential equation (D² - 6D+9)y = 0 falls under Prove your…

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Q: Given A B C D f(x) dx = 0 and 11 6 0 ¹² f(x) dx = 11 6 I 11 5 55 6 evaluate S²3f(x) dx - ₁2f(x)dx.…

A: we have to find the integral

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Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

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Q: dx Evaluate: √(x+1) log(x+1) A In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C C In[log(x+1)] + C In 10…

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A: To evaluate the given triple integral.

Q: Solve the integral: Seln(2x² + 3x-4)³ (4x + 3)dx A eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) (2x²+3x+4)4 B…

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Q: If 9 = {(1, y) |1 ≤ x ≤ 3,3 ≤ y ≤ 6}: D then: 11,3 dr dy

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Q: Solve for the area of the region bounded by x² = 4y + 4 and x = y = 2 (A) none of the choices 128 B…

A: