Use Lagrange multipliers to find the minimum value of the function f(x, y) = x² + y² subject to the constraint zy = 2. Minimum:

Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.…

A:

Q: Direction: Please include your complete solution.

A: Question 1Slope=6x02​−6x0​Question 2The equation of the tangent line is y=2x+5. See explanation for…

Q: Q.2

A: The answer is given below.Explanation:

Q: Consider the following. -2 15 10 y f(x)=16 (4, 16) 5 g(x) = x² x 2 4 (a) Form the integral that…

A: a. ∫04​(16−x2)dx​b. 3128​Explanation:In the graph, we can find the area between 2 curves using the…

Q: (8 points) Suppose the terrain of a hillside is represented as the graph z = f(x). Suppose f(a) = c…

A: I have given detailed solution below thanksExplanation:Step 1: Step 2: Step 3: Step 4:

Q: Evaluate the integral. (Use C for the constant of integration.) cos dx COS -x cos-sin()+C x

A: The given integral is .We can solve this integral by integrating by parts formula method.Integration…

Q: 3x3 +5y3 lim (x,y)-(0,0) x² + y²

A: To find the following limit.

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(6rs, s² 7r). Use the table of…

A: We need to find .

Q: Find f'(x). f(x)=7ex+2x-5 Inx

A: The objective of the question is to find the derivative of the function f(x)=7e^x+2x-5 ln(x). The…

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

A: The given total inventory cost function

Q: The demand curve for original Iguanawoman comics is given by q =  (398 − p)2 50       (0 ≤…

A: The objective of this question is to find the price elasticity of demand when the price is set at…

Q: If 0=28°, find the distance between two cities, A and B, to the nearest mile. The radius of the…

A: The objective of this question is to find the distance between two cities, A and B, given the angle…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: a. 40b. 0c.5​1​Explanation:a. We can evaluate the limit by direct substitution. This means we will…

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A: Answer :(a)  62   (b)  423​Explanation:For any query please ask in the comment box.

Q: Q1 The price of selling x units of item is p(x) = 56 - x. The total cost of producing a items is…

A: Question No. (1): The price of selling x units of item is . The total cost of producing x items is…

Q: Given log x =α, logx x =ẞ, log¸x =y, log¸x = 0, and x 1, find log abcd empt left to earn the full…

A: Thus, \log_a(abcd) = 1 + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\theta}.Substituting these…

Q: Find the area under the curve y = √√2x + 3x from 1 to 3.

A: 15.9562Explanation:

Q: In this problem, p is in dollars and x is the number of units. The demand function for a product is…

A: Part 1: AnswerThe consumer's surplus is $30.Explanation:Dear student, below is the complete answer…

Q: 2 sin x+3sx=3 Write your answer in radians in terms of π. If there is more than he solution,…

A: c

Q: All solutions of the differential equation  y' = −6 − y4  are decreasing functions.

A: The given differential equation is y' = -6 - y^4. The derivative y' represents the rate of change of…

Q: Next Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.03q2 + 3q- 44,…

A: Given:a profit function given by P(q)=−0.03q2 +6q−48 where q is the number of thousands of pairs of…

Q: 1 2x STAR -1

A: y(x)=1e2x−1dydx=ddx1e2x−1Using the Chain Ruleddxf(g(x))=f′(g(x))g′(x)Using the power…

Q: Find a set of parametric equations for the rectangular equation y=4x-4 that satisfies the condition…

A:

Q: Please review and solve problem 6 part 'a' and 'b' and explain how the answer was found. Problem…

A: The answers are attached.Explanation:Step 1:

Q: Q/Derivatives of inverse Trig functions 3 = √√ si y = sin(cos-¹√√1 – In(x − sin x) -

A: The given function is

Q: 5. A company is increasing the production of a product at the rate of 25 units per week. The demand…

A: The objective of this question is to find the rate of change of the profit with respect to time when…

Q: Suppose that the Quick-Fix Car Service franchise finds that the income generated by its stores can…

A: Therefore, the required answer is $2,802,379Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Express log3A, where A = numbers. 14 4 in terms of the logarithms of prime 7 √20 √/148 attempt left…

A: Refer the image posted in explanation for the answer .If you have any further questions or if…

Q: Solve the system of equations 2x - 8y = 148 1x9y=152 by converting to a matrix equation and using…

A:

Q: Solve the given integral equation or integro-differential equation for y(t). y' (t) +27 (t-v)y(v)…

A: The objective of the question is to solve the given integro-differential equation for y(t). The…

Q: A curve has an equation  y=2x2+5x+c where c is a non-zero constant. Given that the roots differ by…

A: ANSWER: c = -11/8Explanation:To find the answer, first we must find the roots of the quadratic…

Q: Use the Chain Rule to find dw/dt. dw dt = w = In x² + y² + z², x = 3 sint, y = 8 cost, z = 6 tan t

A: So, After the differentiation the final answer for the question is:…

Q: Let P = (a, b, c), Q = (b,a, c) and R = (c, b, a), where a, b, c € Z. (c) Find the Cartesian…

A: The objective of the question is to find the Cartesian equation of the plane containing the points…

Q: C. Find the equation of the plane that passes through the points A(1,-1,1), B(1,2,0) and C(0,1,-1)

A:

Q: Əz Əz and at Use the chain rule to find as || 8」8 z = tan (#). u = 7s + 9t, v = 9s - 7t

A: answers are given below.Explanation:

Q: A company selling widgets has found that the number of items sold, a depends upon the price p at…

A:

Q: Solve. log 3x=4 The solution is x= (Simplify your answer.)

A: Log3x=4We have to find value of x

Q: What is the rate of depreciation (in dollars per year) after 5 years? The salvage value S (in…

A: To find the rate of depreciation after 5 years, we need to calculate the difference between the…

Q: Calculate the expected value of X, E(X), for the given probability distribution. -6 -3025 10 E(X) =…

A: E(X) = 1.2Explanation:The expected value of a random variable X, denoted as E(X), for a given…

Q: Let an and ag = 9. n+1 a) Determine whether the given equation is explicit or recursive. The…

A: Recursive means a function that repeats or uses its own previous term to calculate next terms forms…

Q: Use implicit differentiation to find x³+3x²y+y³=8 dy dx

A:

Q: You are looking at a balloon that flies straight up. Your horizontal distance from the balloon is…

A: Let the height of balloon is  m and x m be the horizontal distance The figure

Q: (a) Let v(t) be a differentiable vector valued function of t. If v. (dv/dt) = 0 for all t, can we…

A: The objective of the question is to determine if we can say anything about the magnitude of a vector…

Q: (c) [6 pts] In(x + 1) In(1 - x) = 2. I (d) [7 pts] 2.31-2x = 7.64+x

A: Question cx = 0 and 3 Question dx=−3ln(3)+ln(2)3ln(2)+3ln(3)+ln(7)​≈−1.835Another way of expressing…

Q: lim 2xy +5yz + 3xz (x,y,z) (0,0,0) 4x2 + 25y²+9z²

A: To find:-

Q: +0+x (4) lim xx

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The answers are as follows: (a) The vector equation of the plane is r.(−9,15,10)=−23. (b) The…

Q: When the cross product between any two vector is zero then these vectors are perpendicular Ignore…

A: Give statement "When the cross product between any two vectors is zero then these vectors are…

Q: sine and cosine to which variable it should correspond to?

A: Clockwise Motion: If a particle moves clockwise around a circle, the angle it makes with the…

Q: Use the result, "the set of parametric equations for the ellipse is x=h+a cose, y=k+b sine" to find…

A: