Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: t Let f(x) = 4x4 + 6. (a) Use the limit process to find the slope of the line tangent to the graph…

A: NOTE: Refresh your page if you can't see any equations. . the given value is x=4 the point on…

Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: 2) y" - y' — 6y = 0. бу

A: Follow the procedure given below.

Q: ∞ Determine whether the series (-1)-In -1/3 is absolutely convergent, conditionally conver- n=1

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: Find the radius of convergence and interval of convergence of the series n=1 (x - 5) n n5n

A: Radius and interval of convergence

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n): = 8i + 7…

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Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

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Q: Ga. Draw a direction field for the given differential equation How do solutions appear to behave as…

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Q: write on paper for upvote please. Provide Exact

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Q: Find the intervals where the curve is increasing and where it is decreasing. Also, find all z values…

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Q: Write an equation for the function graphed below -7 6 5 4 -3 -2 y= 50 on it'st 72 3 Q

A: Topic = Functions

Q: Consider the following second-order differential equation. 3y" + 2y' + y = 0 Find all the roots of…

A: We have to find the general solution.

Q: Consider these three examples: A. S 1dx 1+x² B. f sin²x C.S.sin x dx We want to solve one using a…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Write the expression in algebraic form. [Hint: Sketch a right triangle, as demonstrated In Example…

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Q: *T/2 10 cos(0) r dr de

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Q: 2) Evaluate |x + 11 dx

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Q: Write an equation for the function graphed below 13- 12- 1 - 5+ ++ -7 -6 -5 -4 -3 -2 -2 1-1 HE A 1 2…

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Q: Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x²…

A: In this question we have to find the gradient of the function. Note: As per our policy we can solve…

Q: Identify the type of solution for the problem and solve for the general equation

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Q: The function is not one-to-one. Delete part of the domain so that the function that remains is…

A: Here we have to find the inverse function.

Q: Question 28 to determine the instantaneous rate of change of 3, to the nearest tenth.…

A: Explanation of the answer is as follows

Q: 2 Solve the following ODES by Inverse Operator method. 1.2 y - 2y +y = e sinx "LI X Xx Ans:…

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Q: Find the area of the region bounded by the graphs of the given equations. y = 6x-x², y = - 2x The…

A: The given curves are: y=6x-x2, y=-2x   Now find the point of intersection between the given curves.…

Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: Sketch the region R whose area is given by the iterated integral. L1²5-1² dx dy

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Q: State the range of f(x)= {v=Ry>} b. ve Rly - } 3 a. 1 3x+4 C. {v=Ry>0} d. {ve Rly 0}

A: We can find the range as below.

Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (12, 0) Vg(12, 0) =

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Q: Solve a part only

A: Given the function y=2-xx2 Here, student asked part a) only, hence we are answer part a) only.

Q: Use Properties of Exponents and Properties of Logarithms to simplify and the following expression…

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Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x>0x2-1if x≤0

Q: Using Desmos or other graphing software, sketch the graph of y = sin (2x). a. Using the tangents,…

A: Y=sin(2x)

Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: Find y" in Exercises 71-78 1 X 71. y = 1 + 3

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: 9. Consider the function y = 22 with derivatives 2(6-2) dr² Find any horizontal asymptotes of the…

A: Concave Up , if the second derivative is positive . Concave down , if the second derivative is…

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: We need to fill in the blanks.

Q: Consider the following. [[X] = Sketch the graph of the function. Use a graphing utility to verify…

A: Here we have to sketch the graph and then finds its domain and range.

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: Given that      differential equation   6y''+y'-y = 0      ,        y1= ex3         and…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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