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, 2) = xyz; x² + y² + z² = 243 The maximum value of f is The minimum value of f is i The extreme values occur when.x = + y = + and z = +

Q: Find the derivative of 1-3)* (t3 -8) ,t # 2 2-t

A: Explanation of the answer is as follows

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A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

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Q: 5y+10=4y-10

A: 5y+10 = 4y-10 Now add 10 to both sides then we have, 5y+10+10 = 4y-10+10 5y+20 = 4y Now subtract 20…

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A: Let's find.

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Q: х ах 13. S- (6х-x2-5)2 3

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A: Here, form the given figure: A=∫04(0-(0.75x2-3x))dx=∫043x-0.75x2dx

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Q: 2 = e" cos u = e – r, v= re".

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Q: +2

A: To evaluate the given integral.

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A: This question can be solved using the concept of relation between rectangular and polar coordinates.

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Q: 3. The standard fom of the first order lincar differential equation xdy + (2.xy -3y-4x dx =0

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Q: (1) Use the following graph of f(x) for the problems on this page and the next page. 15 10 10 15 20…

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Q: whole number.)

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A: To find the limit of a function in two variables

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A: Solving

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A: