Find and classify the critical points of f(x, y) = 3xy - x³ - 2y².

Q: The function f(x, y) = x³ sin is a homogeneous function of degree a. 1 b. 2

A: given  f(x,y)=x3sin(yx)for homogeneous function   if f(λx,λy)=λnf(x,y)  than degree is n

Q: Let F(x)= = =[ −7 cos(t²) dt. Use the Fundamental Theorem of Calculus to find F'(x). F'(x) =

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Q: Find sin 2x, cos 2x, and tan 2x if cosx= 1/sqrt5 and x terminates in quadrant IV

A: Topic - Trigonometric identities we are given, cos x=15in IV quadrant,cos x >0sin x<0tan…

Q: 2. If cos a = sin ß = ²³, P(a) € QI, P(ß) € QIII, find the following: c. sin(2a) (* e. sin (2) b.…

A: Note  :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 63. Determine the radius and interval of convergence of Σ (21kx)* k=0

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Q: The parametric equations represents a line. Without eliminating the parameter, find the slope of the…

A: given parametric equation of line is  x = 9 t -7     and   y = -5t -1 then we have to find slope of…

Q: Suppose parametric equations for the line segment between (3, 0) and (4, — 10) have the form: [x(t)…

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Q: 6. Find dy/dx by implicit differentiation. (a) sin(x+y)=y² cos.x; (b) tan(xy)=x+y.

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Q: Determine the domain of the function of two variables. g(x,y)= 8 y+x² {(x,y) y*)

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Q: could you please write the answer properly please and clearly

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1

Q: [Gradient Vectors] Let f(x, y, z) = x^3z − yz2 . (a) If we start at the point (1, 3, 2), then in…

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Q: Determine the slope of the tangent line, then find the ㅠ equation of the tangent line at t 4 x = 9…

A: To determine the slope of the tangent line, then to find the equationof the tangent line at t=π4.x=9…

Q: Sketch a graph of x = -5 -4 -3 -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5 - 2t2, y = t - 1. 1 2 3 est 4 5

A: Here is the solution.

Q: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

A: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

Q: What amount must be set aside now to generate payments of $30,000 at the beginning of each year for…

A: We are required to find Amount that must be set aside now to generate payments of $30,000 at the…

Q: Find the period, amplitude, and frequency of the following functions. 1. y = 2 sin(3x) 3 2. y = 5…

A: The given functions, 1. y=2sin3x 2. y=5cos34x 3. y=3cos2x We have to find its period, amplitude and…

Q: Consider f(x) = |x − 3| on [0, 5]. Find all c so that f(c) = fave where fave is the average value of…

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Q: Show if the following limits produce an indeterminate form. Then, evaluate the following limits. x 2…

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Q: The marginal cost function associated with producing x widgets is given by C'(x) = -0.6x + 100 where…

A: Given query is to find the cost of producing first 100 unit.

Q: 2) Find the following: a) f(x, y) = x³y + exy², find i) fxy and ii). b) Suppose that w = Əw Əw find…

A: As per guidelines,  I can answer one question and maximum three subparts of a question.  Since you…

Q: Find the area of S, which is the portion of the plane 2x + 3y + 4z = 28 lying above the rectangle 1…

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Q: Let F(t) = < -1² + 5, t4 + t, In a. Determine the coordinates of the point on the curve traced out…

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Q: to go to obtain an increase of Problem 2. Consider the function f(x,y) = y ¹ | ²₁ (a) What is its…

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Q: Solve the given LDE using the method of variation of parameters.  (D2+1)y = csc x

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Q: an || 2n () 2

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Q: The equation of motion for a particle moving along the y-axis is given as y(t) = 2t² - 8t + 3 for t…

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Q: The solution of the D.E. xdy - ydx = x² + y²dx is 2 a. y-√√x² + y² = cx² O (a). c. y+√√x² + y² + cx²…

A: Given: xdy-ydx=x2+y2dx

Q: A -| n=3 n 3"

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Q: So I've √x 2 xcosy y³ dy dx

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Q: If f(x)=(², what is f'(-1)? (Note: Round your answer to the nearest integer.)

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Q: = 18. Evaluate SF · dỡ, where ♬ = (eª,xy) and C is the curve parameterized by r(t) = (t², t³), 0≤ t…

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Q: Given: F(t)=L-1{s+2 / s(s2+4)} Find: F(pi/4) Choices: 1, -1, 0, 3/2

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Q: 2) Solve for x : a) e* = 80 b) 3¹-* = 9²x g2x

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Q: a) Find the antiderivative of F(x) = cos(x) + e^2x + 2x. b) Find a function f(x) such that both…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question . If…

Q: 22. If log(x) = -4, find the value of log(ar³).

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Q: Suppose a state lottery prize of $4 million is to be paid in 20 payments of $200,000 each at the end…

A: Given Lottery prize $4×10⁶ Paid in 20payment of =$200000each  Time period= 20year  Rate =10%annually

Q: find the length of y=√x² from to += 12 x = formula 3 L = So 9 Ht( f (x) J² dx

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Q: 7. Find the area of the triangle with B = 83°, a = 7 ft, and c = 12 ft.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Question Convert the equation r = 6 cos(0) + 3 sin() into an equation in rectangular coordinates.…

A: in polar coordinates   x=rcosθ   and  y=rsinθr2=x2+y2given  r=6cosθ+3sinθ

Q: 1 Solve for the differential of y when y=sin (1x). x= 3 and dx = N|H

A: The given function y=sinπx. We have to find the value of the differential dy, when x=13 and dx=12.

Q: A certain index I is a measure of soil moisture. An article described the rate of change of I with…

A: we need to solve the given initial value problem.

Q: Determine the value of when 3f(x) + 4g(x) lim x→2 6ƒ(x) – g(x) lim f(x) = 2, x →2 1. limit = 5 2.…

A: We need to find limx→23f(x)+4g(x)6f(x)-g(x)  given  limx→2f(x)=2, limx→2g(x)=-6

Q: A triangular parcel of land has sides of lengths 920 feet, 330 feet and 914 feet. a) What is the…

A: Given length of side of triangle 920ft, 330ft, 914ft We will use Herons formula to find area…

Q: 8. Find the differential of each function: (a)y=tan(cos.x) : (b) y=- Answer D

A: 8) a) y= tan(cosx)

Q: -8 -6 -15 4-5 S 4 + Ox O Using the graph of f(x) above, answer the following. If a limit or…

A: Given Graph:-

Q: Find the curve in the xy-plane that passes through the point (4,6) and whose slope at each point is…

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Q: Suppose Evaluate each of the following limits: (a) (c) lim f(x) = -3, x-a lim f(x)]² lim /h(x) x-a…

A: given  limx→af(x)=-3limx→ag(x)=0 and limx→ah(x)=8accorging to bartleby guide line we do only first…

Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: 2y"+y'-6y=0?

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is

Q: 1. y = sin 4x 2. y = cos 5x 3. y = sin x

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