Solve the following differential equations: 1 √1-3x (a) -dx + sin y cos 2y + 1 dy = 0 (b) x²y + x³ Inx=1-3xy

Q: dx Consider S= using rationalizing substitution. x1/2 + x2/3 Find the integrand in terms of z. A…

A: find out the integrand in terms of z.

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 4 with initial vector

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Q: If the function u = 2e^u e^2u 1/2 Other: In (2² +2²¹²) then ro + you is 4

A: First we calculate partial derivative.

Q: Find all points on the curve y = x3 + 2x2 -6x +5 where is the tangent is parallel to the line 2x + y…

A: The given curve y=x3+2x2-6x+5

Q: The volume, when the curve y = √3+ x2 from x = 0 to x = 4 is rotated about x-axis is O100m cu units…

A: Given:    y=3+x2 from x=0 to x=4  Volume of the curve V=π∫abfx2dx

Q: Laplace and Inverse Laplace Transform Please show clear and complete solutions and choose the best…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: 3. A rectangular plate is submerged in water as shown below. The top of the blue region is the…

A: Given

Q: 13. Water is spilling out of a tank with a leak at the bottom. After t hours, there are t+ √t liters…

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Q: The volume of y = (3x+1)+,x=0, x=8,y=0 O (28/9) TL O (26/3) T O (1372/9) O (248/9) m 6 and x = = 2y

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Q: 2 I 2 Vr +25 dz

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Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: y = e√√²t sin√√2t √2 (s-√2)² + √2 A) √2 (s -√2)² + 2 √2 (s + 2)² + 2 B) 2 (s-√2)² + 2 9

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Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

A: This question can be solved using the concept of shell  method.

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

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Q: The power series representation of f(x) = ln(x2-1) is given by Α. 24-1-1x", -1x<1 n=1 n+1 B. None of…

A: To find the power series representation of the given function.

Q: integrate * S(4√r – V√r² – 6√r³) dr 8 ·12 3 r³ – 2/4 r ² + C 5 35 r-ri-24r + C ² 35 24 3²-5r³+²+ C…

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Q: X -S²- VO- The numerical value of dx will be equal to

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Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

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Q: II. INDETERMINATE FORMS COS X X 5. lim x →∞0

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: W (4) Find Laplace Transform F(s) for the variable x or y in the equations a- +2y'-3y=32e³;…

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Q: 5fe* (e-2x)dx.

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Q: A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

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Q: Find the equation of the tangent line to the curve ³+y³ = 9 at the given point (1, 2). a. 4x-2y=10 O…

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Q: The value of f (1) + g (1) is Blank 1 Blank 1 Add your answer [2² cos r² cos r dr = f(r) sinr + g(x)…

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Q: 4. (a) Find (b) Hence evaluate d dx √1+x² X S (1+x²)³/2 dx.

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Q: dt dx dt -2x=4; where x(0) = 1

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Q: In a laboratory experiment, the population P of a microorganism is found to satisfy the differential…

A: The given problem is solved below in detail.

Q: Which ONE of the following statements is CORRECT with regards to the sequences of real numbers? OA.…

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Q: The value of x for which the series Σ- O A. x<2 or 4<x. OB.2<x<3 or 3<x≤4. OC.2<x<4. O D. 2<x<3 or…

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Q: 2. For a given perimeter, what is the ratio of the length to the width of a rectangle that will have…

A: Solve the following

Q: Evaluate Limx→13 x²-1 O a. infinity 5 O b. 2 O C. 0 O d. none of these O e. 2²/33 25

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Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: Let's find revenue function.

Q: 1The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: Solution is given below:

Q: The value of a is Blank 1. [²1² sin³r cos³r dr == where a =.

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Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: of f(x) = ln(x²− 1) is given by 1. <I. list. <x<1.

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Q: where b₁,b2, b3 are constants and 8² w 8² w ឃ 8² w + əx² Əy² az² If web₁x-b₂y-b32, = b+b+b = 1. Show…

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Q: - Find the value of x of which the function f(x) = O a. none of these O b. 1 OC -1 O d. -3 Oe. 3 2-8…

A: Given:f(x)=12x-8

Q: Find all points on the curve y = x³ + 2x² - 6x +5 where the tangent is parallel to the line 2x + y =…

A: Given :y=x3+2x2-6x+5line : 2x+y=4

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: Find -3) 2/2 lim xxx+1,

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Q: Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the…

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Q: U= at ² w + 0х2 8² w dy² where 61, 62, 63 are constants and b₁ +6₂ +63 " 8² w + = W. az² Item 8.pdf…

A: Topic:- application of partial derivatives

Q: If A = {x+|x-1| : xER}, then which of ONE the following statements is TRUE? A. Set A has a supremum…

A: This question is related to set theory, we will solve it using given information.