Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur. f (x, y) = 6x³ + y²; 3 x² + y² =1 NOTE: Enter the exact answers. Maximum : at (?,?) Minimum : at (?,?)

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A: Let f(x)=y=x2      (1)g(x)=y=x          Compare x=x2x2-x=0x(x-1)=0x=0 or x-1=0x=0 or x=1Put value of…

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A: We have to find the volume of the solid.

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A: As per bartleby guidelines we only give first three question answers.

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A: Solve the following

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A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

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A: Topic = Derivative

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A: General form a polynomial of degree n is P(x) = anxn+an-1xn-1+...+a1x+a0, an≠0  and the factored…

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A: The given problem is solved below in detail.

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A: Given :Diameter of cylinder= 6 mHight of cylinder = 7 m

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A: We have to find integrating of given Questions

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Q: 4 The net signed area in the above graph can be written as (mæ + b)dx, where c = d and b = = U

A: The net signed area in the above graph can be written as ∫cdmx+b dx, where c=?,  d=?m=?, and b=?

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Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

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A: topic- indefinite integral

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A: Given g'(x)=1x2+1 Integrating on both sides, we have ∫g'(x) dx=∫1x2+1 dx

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A: Topic:- simplification

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A: Here, the given functions are: f(x,y,z)=x4y+z4, x=st2, y=st,z=s2t

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A: Take a homogenous equation and first differentiate then simplify

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A: The integration of the integral is cos(4x)cos(2x).

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A: We need to provide 5 sample problems for Elimination of Arbitrary Constant Differential Equation.

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A: Evaluate the limit using the limit law for a quotient

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A: Let T represents temperature of thermometerand S be the constant temperature of oven.  t represents…

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A: Let's find.

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A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

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A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 &amp; x2=8

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A: Differential equations

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A: see below the answer and calculation

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A: Given :f(x,y)=x3y-xy3

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A: fx is differentiable and invertible function so that f(3)=4 and f'(3)=12

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