Method of undetermined coefficients y" -y = 3et ○ y = ₁₁e² + c₂e²x + ²√xex O y = c₁e¹ + c₂e²x + 3xe* y = e² (c₁ cos x + c₂ sin x + 2xe*) O y = C₁ cos x + c₂ sin x + xex

Q: Evaluate each integral. √x+Yy dz Jx - "X rx + y 0 Jx-y y dz dy Now evaluate J = = y dV, where E =…

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = 4 + xy - x - 2y, D is the…

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Q: Find the largest open interval where the function is changing as requested. 24) Increasing…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = =…

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Q: Consider the following equations. 124 O Sketch the region bounded by the graphs of the equations. y…

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Q: The position function of a particle is given by the equation s(t) = -2t2 + 3t + 10. Determine the…

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Q: Q2) A: By using partial method solve [2x² cos x dx

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Q: Determine the volume of the solid under z = 4xy + x² over the rectangle R= [1, 2] × [0, 3]. [Show…

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Q: 6. Find the area of the region bounded by x = y³ − 4y² + 3y and the x = y² − y. 77 (a) A= square…

A: The region is bounded by the curve x=y3-4y2+3y and x=y2-y

Q: ror(4)). 95. Find the restrictions in the domain, if any, for If there is more than one restriction,…

A: Note: The first question that is question 90 seems incomplete. So, solving 95 for you.

Q: a-limx-4(2)

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Q: Find the area enclosed by the curves f(x) = 33 - x² and g(x)=x². The area (rounded to two decimal…

A: The region bounded by the curves fx=33-x2 and gx=x2

Q: d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the given integral by changing to polar coordinates. sin(x² + y²) da, where R is the region…

A: Given that,

Q: 6. fx√4x+1dx

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Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

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Q: When using Runge-Kutta method of order 4 to solve the initial-value problem: ý= 2, 0≤t≤ 1, y(0) = 0,…

A: We have to find K2 for w3.

Q: Sketch left-endpoint and right-endpoint approximations for f(x) = on [1,2]; Approximate the area…

A: fx=1x on 1,2, n=4

Q: Find the sum of the values of f(x) = x³ over the integers 1, 2, 3, ..., 10.

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Q: Q1\A: Find the value of K in the following linear system which is make the solution failure Kx+3y=6…

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Q: By using partial method solve [ 2x² cos x dx

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Q: SUBJECT: DIFFERENTIAL EQUATION TOPICS Growth/Decay  Newton's Law of Cooling/Heating Mixture Simple…

A: Given that, A tank has pure water flowing into it at 10 liters/min. The contents of the tank are…

Q: Solve the following differential equation Ỳ − (sinx) y = 2 sinx

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Q: Find the integral of the following indefinite integral equations: Jx dx / (5 + 9x4) Jx dx/v(16-9x4

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Q: Find the equation of the tangent line to the function f(x) = 3** at x = 1. (Use symbolic notation…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

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Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: D Operator: Solve the DE y" - 7y" +14y - 8y = 0 y = c₁e¹ + c₂e²x + c3e4x Oy=c₁e²x + c₂e4x + c3e6x y…

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Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: The base of a three-dimensional figure is bound by the line y = x + 4 on the interval [-3, 1].…

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Q: (C) For what values of x does the series 11=1 (D) Find Taylor series at x=2 for the function ala…

A: series and taylor

Q: -0.1 Using the Trapezoidal rule, the approximated value for the integral: √1+x dx, is equal to о о 1…

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Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: We have that the center is 4+i. So, we have the LHS as |z-4-i|. We see that (7, 0) is on the curve.…

Q: 10. Find r(t) if = (4t3+ 4t)i + 6tj + 3t²k, r(0) =i+j.

A: We have to find out r

Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Using linear approximation at x=a L(x) ≈f(a) + f'(a)(x-a)

Q: 4. Solve the following DE using a suitable type of transformation. y' = x + y (let v = x + y) O y =…

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Q: Let [ f(x) dx = 5, -6 Find and -3 [ f(x) dx = -4.5 -4.5 -3 6 (5 f(x) - 6) dx = f(x) dx = 6, f(x) dx…

A: The given integrals are;  f(x) , limit from -6 to -1.5. f(x), limit from -6 to -4.5. f(x), limit…

Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8²+45-23) (s²+45+13)³…

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Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

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Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

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Q: ƒ (t) = -{ 5,03

A: We know the followingLf(t)=∫0∞e-stf(t)dtLeat=1s-aLtn=n!sn+1Lsinat=as2+a2Lcosbt=ss2+b2

Q: Consider f(x)=x*. Find the first derivative, f'(x).

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Q: 17. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the…

A: Concept of similarity along with derivative is used.q

Q: 9. Integral (2x-5) dx x²5x+3

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Q: Find the solution of the initial value problem y" + 6y' + 10y = 0, Y (²7) = 0, y¹ (7) = 9. 2 y(t) =…

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Q: Using the Simpson's rule, the approximated value for the integral: f, dx, is equal to -3 0 6 None of…

A: A detailed solution is given below.

Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: Use the formula for the binomial series: to obtain the Maclaurin series for V1 + x. Ο 1- O Ο 00 1 +…

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Q: What is the area under the graph of y = 2 54-3-2-1 O O N/W 13 2 15 2 ਜਾਨ , -2+ -3 4 1 2 3 4 5 X on…

A: The region is bounded by the graph y=2-x on the interval -2,1