The given differential equation is already in standard form, as the coefficient of the highest order derivative is 1. W₁ = The next Wronskians to calculate use y₁ = ex and y₂ = e-2x that we identified from the complementary function and the function of x that makes the equation nonhomogeneous, f(x) = 6 + ex = W₂ = y" + 3y + 2y = = 0 Y2 0 e-2x (6 + ex)-1 -2e-2x Y₁ 0 6+ e* e-x 0 -ex (6 + e*)-1|

Q: (a) Find the averge value of f(x, y) = curves y = 0, y = x², and x = 1. xsin y over the region D…

A: Solution: f(x,y) = xsin(y)

Q: Write an expression in factored form for the polynomial of least possible degree graphed below. 3- W…

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Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

Q: (e) Find the linear approximation of the function f(x, y, z) = x³ √√y² + z² at the point (2, 3, 4)…

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Q: Given the diagram of the bounded area, The limits of integration Choose Area in square units is X is…

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Q: Match the following iterns for the integral of (12) Using partial fractions, the above integral has…

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Q: 1) Solve the following ODES by Undetermined Coeff. ● 4X 11 X y - 16 y = 19.2 € + 60e, y(a) = y() -4X…

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Q: Write an equation for the function graphed below 5+ 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 y = -5+ 1…

A: topic- graph of a function

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

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Q: (b) Identify (3) and g(3). f(3) = g(3)= (c) For what value(s) of x is f(x) = g(x)? x= (d) Estimate…

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Q: lim n→∞ - 17n + 11 11"

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Q: Examine the function for relative extrema. f(x, y) = 2x² + 7y² - 4x − 14y + 12 (x, y, z) = ((No…

A: Given function: fx, y=2x2+7y2-4x-14y+12

Q: Umm can this be answered more clearer, I can't really tell what the answer is, and when I put it in…

A: Let's solve.

Q: Consider the function f(x) = √x. (a) Find the first and second Taylor polynomials for f at x = 1 .…

A: Given : taylor series =fx=f(x0)+f'(x0)(x-x0)+f"(x0)(x-x0)22!+..........     first taylor polynomial=…

Q: Evaluate the integral. (x6 + 4y³) dy

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Q: Write an equation for the function graphed below 4 y = 3+ 2+ 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3- -4 -5+…

A: topic- equation of a function

Q: Module A car dealership increased the price of a certain car by 4%. The original price was $44,400.…

A: As per given question  We have to determine new price of car

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Consider the following function. f(x) = 4x² - 7x² Determine whether the function is even, odd, or…

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Q: The profit from the supply of a certain commodity is modeled as P(q) = 30 + 50 In(q) thousand…

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Q: What is 6x² dx?

A: We will solve it

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: L(t) The vector parametric equation for the line through the points (1, 2, 4) and (5, 1,-1) is

A: Given points,  (1,2,4) and (5,1,-1)

Q: Find all values for which the function discontinuous. X-1 if X41 o if 18x44 X-2 if X>4 f(x);

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Q: 5. Use an iterated integral to find the volume of the solid that is bounded above by the plane…

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Q: Find the domain of the function. (Enter your answer using interval notation.) F(x)=√x + √7-x

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

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Q: Evaluate the following limit using Taylor series. 3tan ¹x-3x+x³ 5 lim x-0

A: Follow the procedure given below.

Q: For the given differential equation, what is the a) order, b) degree of the differential equation,…

A: The given differential equation is d3ydx35-7xd2ydx23+5dydx=11ey

Q: Four partners are dividing a piece of land worth $159,200 among themselves using the lone-divider…

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Q: Find the area between the curves. 1/5 6/5 y=x y = 4x¹ The area between the curves is (Do not round…

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Q: The figure shows the temperature values (in °F) on a typical May day in a certain Midwestern city. t…

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: (x + y) dx + (3x + 3y - 4) dy = 0

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Q: Sketch the region R whose area is given by the iterated integral. To Se *6 *3 7- 6- 5- 4- 3- نيا 2-…

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

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Q: 11) The inequality 3x-2 0 3x² - 9x x-2 d. <0

A: Given, 3x-2&lt;x+4x-2

Q: Can you please handwrite the answer, I can't read whatever it is he typed.

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Q: Find three positive numbers whose sum is 114 and whose product is a maximum.

A: follow the procedure given below.

Q: A force of 660 newtons stretches a spring 3 meters. A mass of 55 kilograms is attached to the end of…

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Q: A math teacher won a lottery that pays $1,000 per month for the next 20 years. But, he prefers to…

A: To find out the amount that the teacher will accept now.

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Given that log a ( 2 ) = m and log a ( 3 ) = n , write exact expressions in terms of m and/or n for…

A: Write expression in terms of m and n for each of the following.

Q: Find a possible formula for the trigonometric function whose values are in the following table. y =…

A: topic- trigonometric function

Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).