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Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

Calculate the area, in square units, bounded by g(x)=4x+8 and
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Write the iterated integral for a sphere centered at (0,0,0) with a radius of 2. Use the order dz dx...

Product


Radius (inches)


Height (inches)


Volume (cubic inches)




Baking power


1.25


3.65

...

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Can somebody help me on how to evaluate the integral.

Use​l'Hôpital'sRule to find the following limit.

Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67.Additional MaterialseBook

f(x,y,z) = 2x + 7y + 9z and g(x,y,z) = x2 + y2 + z2&nbsp;Approach:<ul><li>We will make use of the method of Lagrange multiplier to solve this.</li><li>The solution will be the solution to the system of equations generated by:<ul><li>&nabla;f(x, y, z) = &lambda;&nabla;g(x, y, z) and</li><li>g(x, y, z) = 67</li></ul></li></ul>

f(x, y, z) =2x + 7y + 9z = (2x, 7y, 9z)Hence,&nbsp;&nabla;f(x, y, z) =(2, 7, 9)g(x, y, z) = x2 + y2 + z2&nbsp;= (x2&nbsp;, y2&nbsp;, z2)Hence, &nabla;g(x, y, z) = (2x, 2y, 2z)Hence, &lambda;&nabla;g(x, y, z) = (2 &lambda;x, 2 &lambda;y, 2 &lambda;z)

Hence the system of equations to solve are:∇f(x, y, z) = λ∇g(x, y, z)That is (2, 7, 9) = (2λx, 2λy, 2λz)Or, 2 = 2λx; 7 = 2λy...

Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

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Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

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