Approximate the area under the curve y = x² from x = 1 to x = 3 using a Right Endpoint approximation with 4 subdivisions.

Q: 3. (6x + y²) dx + 2x - 3y) dy = 0. ANS. 3x + xy² ya:

A: Here we have to solve the differential equation.

Q: Find the exact sum of the following series (0.25)" (0.25)³ Σ(-1)n-1 n 3 n=3 (0.25)4 4 + (0.25)5 _…..…

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Q: Find a and b such that ƒ(x) = x² + ax + b 8 17 has an average value of 933 over [0,1] and an average…

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Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: Bottom of the page is cut off i cannot see the solution.

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Q: What region R in the ry-plane minimizes the value of the following expression? f (x² + y² - 9) dA R…

A: The given double integral ∫∫Rx2+y2-9dA we have to find the region R on the  xy-plane that minimize…

Q: Q5)-Solve the following a)- 3|4x-1| ≤ -9 (draw)

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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Q: Set up the double integral that solves for the area of the region that lies inside r = 3+2 cos θ and…

A: Given:          r=3+2cosθ , r=2

Q: Find the number(s) b such that the average value of on the interval [0, b] is equal to 6. f(x) = 6x²…

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Q: Let g be defined by the equation g(x) = sin 2 dt 1²-1 Show that g'(x): = sec z.

A: Given:       gx=∫sinx0 dtt2-1       Factor -1 from the denominator:       =-∫sinx011-t2dt       The…

Q: Show the complete solutions, kindly include all the necessary drawings, graphs and illustrations.…

A: We have to find the orthogonal trajectories of circle through the orgin with centre on the x axis

Q: Answer is wrong

A: Note: Since, the unit of the radius is not given, we have assumed that the unit of the radius of the…

Q: Evaluate [C 02 6 3 10 160xy³ dydx

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Q: 5. Solve the given differential equation. (Recommend using Variations of Parameters) y"+3y'+2y =…

A: Given that, the differential equation is y"+3y'+2y=sinex. Obtain the complementary solution.…

Q: If the region occupied by a lamina is symmetric with respect to both the x- and y-axes, then the…

A: Solution: Consider the mass of the lamina ∫∫R ρ(x,y)dA

Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Find the area of the inner loop of the limacon given by r = 1+2sin 0.

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Q: Find the power series representation of the function f(x) = = x 2x² +1'

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Q: At what points is the following function continuous? f(x) = 3 x - 512 2 X-64 12, 7, x8, x-8 x=8 X =…

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Q: Consider the function f(x) this interval. 1 on the interval [5, 11]. Find the average or mean slope…

A: Given, f(x)=1/x

Q: Evaluate the definite integral and choose the correct answer. dx 1+5x 0 1 O -In 11+ 5xl + C 5 1 1+5r…

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Q: a. y=sin(x² + 3x + 1)

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Q: Question Find the average value of f(x) = 5 cot (x) csc (x) - 2 over the interval [] Submit an exact…

A: As we know that; The expression for the average value of the function over the interval a,b is:…

Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

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Q: y' = CSC x y cotx

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Q: (y² - 2xy + 6x) dx − (x² − 2xy + 2) dy = 0. ANS. xy²x²y + 3x² - 2y = c.

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Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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Q: Use implicit differentiation to find dy dx x3 + y = 15xy || dy dx

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Q: Solve the differential equation: dy = A - By. Find the general solution to the dx differential…

A: We need to find out the general solution and particular solution for the given differential…

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: If f(x) = 2ln(8 + x), f'(x) = f'(3) =

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Q: Question 4 L² (1-1²) ³ds

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Q: a. b. n=1 8 n någn-1 (-5)n 1 nVn? +1

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Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: For each differential equation, indicate the order as a number. d'y dt4 Order is: d²y dt² Order is:…

A: Yo find the order of differential equations.

Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) 200+600t 120t², where t is in…

A: The traffic flow rate across an intersection is rt=200+600t-120t2, where t is in hours and t=0 is 6…

Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: y= e2x+1 e-1

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Q: (1 + y²) dx + (x²y + y) dy = 0.

A: The differential equation is given by 1+y2dx+x2y+ydy = 0                               ........1 To…

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: Can you write out the solution in a better format please

A: Integral of (cot(x)csc(x) = - csc(x)   Csc(π/2) = 1 Csc(π/3) =2/√3

Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

Q: Find the general solution : (3x + 2y + 4) dx + (3x + 2y - 3) dy = 0

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: 3. Express the integral I = f(x, yz) dV as an iterated integral in three different ways, where E E…

A: Solution is given below:

Q: In which limits below can we use L'Hospital's Rule? lim 818 Olim 848 Olim 48 Olim €8 et X In x e X H…

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