Use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. f(x, y) = x² + y², (x - 1)² + 4y² = 4 maximum value minimum value

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Q: 5. [3] Determine the value of k when x³ + kx² + 2x -3 is divided by (x-1) and the remainder is 2.

A: Solve division method

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A: Given:- f and g are two differentiable functions

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Q: Make an ORIGINAL EXAMPLE OF "Variable Separable" A) GIVEN B) SOLUTION C) ANSWER D) WITH EXPLANATION

A: Given expression, Solve 1+x2dydx=1+y2

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A: givenarea of region 1 is=26

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A: 2xy-3x2dx+x2+2ydy=0

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Q: 12. If $5000 is deposited in a bank paying r% interest (r = interest rate), the amount 3 years later…

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Q: 1. Find the derivative of each function. Use proper notation, and simplify your answ This includes…

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Q: x² - 3x Find lim x→3 x2 - 9 2

A: to find out the limit.

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Q: Question 6 Given: y = (16+¹) Z -61² (16+74) 3 √16+t¹ 23 (16+) O (E) None of the choices -21² (16+¹)…

A: Solve for the dy/dt

Q: Based on the given table of data, compute each of the following derivatives (fog)'(2) (gof)(4) = X 2…

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Q: (d) Two boats leave a port at the same time. One boat travels in a direction of N 70°E at 12 mph and…

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Q: Graph the function. Then answer the a) What are the domain and range of f? b) At what points c, if…

A: Understanding of graphs of any function is required to solve this question. Domain of a function is…

Q: Find the following limits. Show all work a) lim x-0 b) lim X-8 c) lim X18 √2x+1-√√x+1 X 2x³-3x+1…

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Q: (d) The area of the triangle AKMN is A=25-√√3 in². If <MKN = 30°, find |KN|=|MN|= ?

A: Given , A(∆KMN)=253.|KN|=|MN|∠MKN=30°

Q: Differentiate the function. 7x²-1 3 4x³ +5 y=- y'=0

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Q: Find the following derivatives. Express your answer in terms of the independent var 3x-3z 2y +3z Ws…

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Q: The graphs of y = 5, y = g(z) (solid) and y=h(z) (dashed) are shown; the graph is not drawn to…

A: Solution is here

Q: Use vector notation to describe the points that lie in the given configuration. (Let s and t be…

A: Given that  The plane spanned by.  v1 = (5, 6, 0) and v2 = (0, 5, 6)   To find :- The vector…

Q: 1. Given the piece-wise defined function f(x) = {* a) lim f(x) = x², x < 4 (x+6,x ≥ 4 b) lim f(x) =…

A: Given query is to find the limit of the function

Q: Derive the following functions x-2 3x-4 44. y=- 5-x 4-2x 46. y=-

A: Understanding of rational function is required in order to solve these questions. Rational function…

Q: If z is a differentiable function of x and y satisfying the equation sin(x²z+ny²) + 2x³ = yz² + 2,…

A: Let's find partial differentiation at given point.

Q: graphed below. Find each value. 10+ 10-9-8-7-6-5-4-3-2 lim f(x) = 2-2 lim f(x)= z→2¹ lim f(x) = I-2…

A: Given graph of fx as below

Q: (b) Find (f ¹)'(1) if f(x) = x² +5 sin " + cos2. (TTX) (X)

A: Solution to find the value of derivative of inverse of f(x) at x = 1 is as follow

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A: Given query is to find the value of x.

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Q: Maximize f(x, y) = √11-x² - y², x + y - 2 = 0.

A: The given function to maximize is: f(x,y)=11-x2-y2 with the constraint g(x,y)=x+y-2=0...(1)

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Q: Question 3 Let P(t) be a deer population (in thousands) of an ecological region t years after 2000.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 13. Find the point (x, y) on the curve y = x² + 1 that minimizes the distance to the fixed poi (4,…

A: Given curve:- y=x2+1 We know distance between points x1,y1,x2,y2d=x2-x12+y2-y12

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form…

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Q: f(x) is graphed below. Find each value. 10+ 9 8 7- 10-9-8-7-6-5-4 f(x) = lim 2115 lim f(x) = lim…

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Q: 5. Rewrite the expression as an algebraic expression in x. X cos( 1¹ (3)). H≤3 |x|≤3 (a) cos sin

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: Explanation of the answer is as follows

Q: At what points is the function y= x+3 2 xỉ - 5x+6 continuous? Describe the set of x-values where the…

A: We can find the x-values where the function is continuous in the below steps.

Q: The graphs of y = f(x) (solid) and y = g(x) (dashed) are shown. The two graphs intersect at (5, 18).…

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Q: The graph below is the function f(x) -5-4-3-2 Find lim z 2 19 NA Find f(2) Z -2 -3 4 f(x) Find lim…

A: Here we have to use the graph to find the limit of the function.

Q: 618 x 99 6182

A: using simple multiplication

Q: 7. Determine all value(s) of the constant k so that the planes x+2y+3z = 4 and 3x + (k²+2)y+(7-k) z…

A: We need to find values of k.

Q: y = tan-¹(7x)

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Q: P(w)=2w^2 -w +4 /√w *Differentiate the function

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Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.