etch the region of integration. (Select the correct graph.) In 5 5 [ins T3 124 af In y dy dx

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

A: We will use standard method to solve this.

Q: The graph below is the function f(x) 5 4 3 12 -5 -4 -3 -2 -1 -1 -2 -3 -4 lim I→2 1 2 3/4 5 a● Select…

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Q: Find the centroid of the region bounded by the graphs of the functions y = 3x², y = x² + 4 The…

A: Centroid Of the Region :           x¯ = 1A∫x=ax=b xf(x)-g(x) dx  and   y¯ = 1A∫x=ax=b 12fx2-gx2 dx…

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 f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: Given F(x, y, z) = ei + (xe + e*)j + ye² k. (a) Show that F is conservative by finding curl F. (b)…

A: use the fundamental theorem of calculus and partial derivative for finding the line integral.

Q: 2. (x+y) dx + (3x + 3y − 4) dy = 0

A: The objective of the question is slove the given differential equation.

Q: Find the limit as k approaches infinity for k ^(1/k)

A: Topic:- calculus

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

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Q: 6) Identify the vertical and horizontal asymptotes of (x)= x-4 - 2x+17 b. vertical-x- 4, horizontal:…

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Q: Find the domain and the range of the function. (Enter your answers using Interval notation.)…

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

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Q: The following table shows worldwide sales of a certain type of cell phone and their average selling…

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Q: lim n→∞ - 17n + 11 11"

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Q: Find the inverse function (if it exists) of f(x) = ln (1-2x). If the function is not invertible,…

A: NOTE: Refresh your page if you can't see any equations. . to find an inverse function, interchange…

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 12ex - 12 y(x) =

A: See  the details solution in below

Q: Evaluate fx² Arcsinxdx

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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: 8) How many solutions does the equation a. 0 b. 1 X+5 x-3 IX 1 || 4 x²-3x C. 2 d. 3 have?

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

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

Q: Find the general solution of the given higher-order differential equation. y"" - 8y" - 9y' = 0 y(x)…

A: The given differential equation is y'''-8y''-9y'=0 ............ (1)  Equation (1) can be rewritten…

Q: Question 4 An artist has decided to finish their piece of artwork by balancing it on a fulcrum and…

A: Given that y=sinπx+4bounded by x=0,x=2 and y=0Solutiuon :centroid x¯…

Q: Evaluate the function at the given value of the Independent variable. Simplify the results. (If an…

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

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Q: We have found the following Wronskians. W = −e-³x; W₁ = −e-²x (4 + ex)-¹; W₂ = e¯x(4+ e*)-¹ Р We…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 2) Evaluate √3|x + + 1| dx

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Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: Solve the given differential equation. x²y" + 13xy' + 36y = 0 y(x) = ,X>0

A: The given differential equation is;  x2y''+13xy'+36y=0.

Q: How much must a person save monthly at an interest of 7.3% to buy a $15,000 car in five years?…

A: We have to find the monthly amount to save.

Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

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

A: This is a problem related to differential equation. Based on the general formula and concept we will…

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: Зу" +y=0.

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Q: (4x²y² - x² + 4xy² - x) dx + (2xy + x + 2y + 1)dy = 0

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

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

A: We need to find y2.

Q: Replacement Time An outboard motor has an initial price of $2,160. A service contract costs $400 for…

A: Topic:- application of derivatives

Q: - The complementary function is १ex . Ус where C₁, C₂, C3, C4 си the particular Solution se = c₁ex +…

A: This is a problem of ODE. Please follow the procedure given below.

Q: Determine whether the integral is convergent or divergent. x² V6+x³ [ convergent Ⓒ divergent If it…

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

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: The graph below is the function f(x) -5 t los 6 Find lim Find lim -4 Find lim 3 on e Z→-1- I→-1 2 1…

A: topic- limits

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

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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: Determine whether the given set of functions is linearly independent on the interval (-∞, co). f₁(x)…

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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: errain difficulties, two sides of a fence can be built for $4 per ft, er two sides cost $8 per ft.…

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Q: Find the real roots of the equation B 244

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z+12=0 and 2x + 4y - 3z…

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Q: Evaluate the function at the given values of the Independent variable. Simplify the results. g(x) =…

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