Use Lagrange multipliers to find any extrema of the function subject to the constraint x² + y² ≤ 1. f(x, y) = exy/4 minimum (smaller x-value) = minimum (larger x-value) ศ 1)-1 = maximum (smaller x-value) maximum (larger x-value) = =

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A: To determine the intervals where the graph of the given function is concave upand concave down.

Q: To complete the process legible

A: To prove the Second Derivative Test for a strict local maximum. We'll assume thatf:Rn→R is a…

Q: 27 sin(t) cos(t) = −12 cos(t) t =

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Q: f(x)= 3ex 2e-5

A: f(x)=3ex2ex−5f′(x)=ddx[3ex2ex−5]Using the quotient rule ddx[f(x)g(x)]=g(x)f′(x)−f(x)g′(x)[g(x)]2

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A: Answer:  gu​(0,0)=17gv​(0,0)=8Explanation:Step 1:

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A: We have to classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.…

Q: Q.6

A: See the answer image (sketch of the region) in the explanation field. The area of the region can be…

Q: Deriving Snell's Law from an Optimization Problem Refraction is a physical phenomenon that happens…

A: Please find the below attached solution as per the suggested steps.Explanation:

Q: Match the following log expressions to their correct evaluation. 1. 5 1+In(e²)-3log2(4) In(e³) 2. 4…

A:

Q: round to one decimal plce.

A: To solve this problem, use the formulas for continuous compounding and annual compounding to…

Q: Consider the following function: 567 X if x-6 f(x) = k+569 if x = -6 (kx)23 if x > -6 For each of…

A: The limit of the function f(x) at x= -6   exist if =

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral with n -…

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Q: If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) h(1) = 5 h'(1) = -7 g(1) = 4 g'(1)…

A: Answer : -47Explanation:Note:f≡f(g(t),h(t))and   fx​≡fx​(g(t),h(t))

Q: Find the area between the curve y = xex and the x-axis from x = 1 to x = 4. (Give an exact answer.…

A: Therefore, the required area is A=21​[e16−e] square units.Explanation:Step 1: Step 2: Step 3: Step…

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A:

Q: Q.3

A: (a) The series INFINITE SUMMATION n=1 of (n²) / n diverges.(b) The series INFINITE SUMMATION n=1 of…

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A: Given that when air expands adiabatically (without gaining or losing heat), its pressure P and…

Q: Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on…

A: The objective of this question is to prove that a function f(x), which is continuous and…

Q: Find an equation of the ellipse with vertices (0, 3), (12, 3) and eccentricity e = Select one: a.…

A: Vertices:eccentricity, e=

Q: Hello Continuing with this problem, shown in the picture, where the parameterization for S was…

A: Hence, the surface area of the parametric curve is 2​πExplanation:Step 1: Step 2:Step 3: Step 4:

Q: Write the corresponding rectangular equation for the curve represented by the parametric equation…

A:

Q: 2 sin x ate the integral using substitution method dx (3 + cos x)5

A:

Q: 7) The region bounded by y= √x, y= 2, x=0 is revolved about the y-axis to generate a solid, its…

A: The objective of this question is to find the volume of the solid generated when the region bounded…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: f′(x)=−(3x−5)23​Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Find f'(x). f(x)=-6 Inx+13x² -7

A: The objective of the question is to find the derivative of the function f(x) = -6 ln(x) + 13x^2 - 7.

Q: Find dy x = p² y = 7-8t Select one: a. dy dx O b. dy ○ c. ။ *| dx dy dx O d. dy dx 16 81 18 I dy…

A:

Q: ☐ Let 60, 61. Which of the following must be true if y = log(x)? Check all that apply. ☐ y = b² 1 y…

A: Option C is correct Option D is correct Explanation:

Q: Find the first partial derivatives of the function 5x f(x, y) = (x + y)²° 1. fx(x, y) = 2. fy(x, y)…

A: 1.fx​(x,y)=(x+y)35y−5x​ 2.fy​(x,y)=(x+y)3−10x​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: A triangular plate with base 1 m and height 3 m is submerged vertically in water so that the tip is…

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Q: Find the absolute extrema of f(x) = 7x2 x-5 on the interval [-1, 2]. maximum, f ; minimum, f

A: on the interval Note:As per bartleby guidelines we are supposed to answer only3 sub-parts (if there…

Q: y = 1x312, 0 ≤ x ≤ 21

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Q: x f(x) g(x) T(X) g'(x) 3 1 9 9 6 7 4 3 3 2 -5 g(x+f(x)), x=3

A:

Q: help with question.

A: The total profit for the second 6-month period is $18660.Explanation:We find the total profit for…

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A: Let x be the side length of base square Let z be the height of the boxThe figure of box

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Q: Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on…

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Q: Use the graph to evaluate the limit. lim f(x) 0+x -B 6 30 2 R X +30 G OA. -3 OB. 3 ○ C. 0 OD. The…

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Q: 1an with a₁ = 2, an+1 = an with a₁ = 3, an+1= 1+sin(n) n 3n-1 2n+5 an an v. vi. n=1

A: (v) Given that the series is                  Thus, the series is convergent by the ratio test.

Q: Consider the equation x25 + y3 + z4 + sin(xy − z) = z2. Find ∂z∂x at the point(1, 2, 2)

A: The objective of the question is to find the partial derivative of z with respect to x, denoted as…

Q: A medical laboratory raises its own rabbits. The number of rabbits N(t) available at any time t…

A: Hence Complete the solution.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Give your final answer in interval notation. Find (by hand) the intervals where the function…

A: The given function is

Q: Hello Continuing with this problem, shown in the picture, where the parameterization for S was…

A: To calculate the surface area of S, we'll use the formula for the surface area of a parametric…

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: help

A: The average value of the function f(x) over the given interval is 3.Explanation:

Q: Suppose that lim f(x)=8 and lim g(x)=-9. Find the following limits. X-2 X-2 a lim [f(x)g(x)] b. lim…

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Q: find y as a function of x if y'" + 81y' - = 0 where y(0) = 1, y'(0) = 81, y"(0) = 324

A:

Q: Solve the following system of equations using any appropriate method of your choosing: • x-y+z=8…

A: The correct answer is:(x,y,z)=(3+2z,-5+3z,z)Explanation:

Q: Q4\ Sketch the plane curve represented by the vector valued function = (3 cost)i(4 sint)j ŕ(t) NA…

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Q: #10 For the surface x³-2xz+y4+1=xy do: (a) Find the tangent plane at point (1,1,1),, Find…

A: (a) Equation of tangent plane at point (1,1,1) is: y=1(b) Equation of normal line at the point…

Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The objective of this question is to find a parametric representation for the given paraboloid S and…