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# quiz9

$There~is~a~3-dimension~graph,~z~=~2x~+~3y~+~5.~If~it~is~projected~to~2-dimensional~(x,~z)~space~while~the~value~of~y~is~fixed~to~10,~what~is~$$~the~equation~of~the~line~in~the~x,z~space?$

$There~is~a~3-dimension~graph,~z~=~2x~+~3y~+~5.~If~it~is~projected~to~2-dimensional~(y,z)~space~while~the~value~of~x~is~fixed~to~15,~what~is~$$~the~equation~of~the~line~in~the~y,z~space?$

$Given~z~=~2x~+~3y~+~5,~find~the~partial~derivative~~\frac{\partial~z}{\partial~x}.$

$~Given~z~=~2x~+~3y~+~5,~find~the~partial~derivative~\frac{\partial~z}{\partial~y}.$

$Find~the~partial~derivative,~\frac{\partial~z}{\partial~x},~of~the~function~z=3x^{2}+2x+3xy+5y^{2}+10.$

$Find~the~partial~derivative,~\frac{\partial~z}{\partial~y},~of~the~function~z=3x^{2}+2x+3xy+5y^{2}+10.$

$Find~the~second~order~partial~derivative,~\frac{\partial^{2}z}{\partial~x^{2}},~of~the~function~z=3x^{2}+2x+3xy+5y^{2}+10.$

$Find~the~second~order~partial~derivative,~\frac{\partial^{2}z}{\partial~y^{2}},~of~the~function~z=3x^{2}+2x+3xy+5y^{2}+10.$

$Find~the~cross~partial~derivative,~\frac{\partial^{2}z}{\partial~y\partial~x},~of~the~function~z=3x^{2}+2x+3xy+5y^{2}+10.$

$Find~the~marginal~productivity~of~labour,~\frac{\partial~Y}{\partial~L},~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~productivity.$

$Find~the~marginal~productivity~of~capital,~\frac{\partial~Y}{\partial~K},~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~productivity.$

$Find~the~second~order~partial~derivative~w.r.t.~labour,~\frac{\partial^{2}Y}{\partial~L^{2}},~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~productivity.$

$Find~the~second~order~partial~derivative~w.r.t.~capital,~\frac{\partial^{2}Y}{\partial~K^{2}},~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~productivity.$

$Find~the~cross~partial~derivative,~\frac{\partial^{2}Y}{\partial~K\partial~L},~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~productivity.$

$Find~all~the~correct~arguments~about~MPL(the~marginal~labor~productivity)~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~$$productivity.$

$Find~all~the~correct~arguments~about~MPK(the~marginal~productivity~of~Kapital)~of~the~production~function~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~A~is~a~constant~representing~$$productivity.$

$The~production~function~is~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~Find~the~gradient~of~the~isoquant~of~the~production~function,~\frac{\partial~K}{\partial~L},~given~the~value~of~Y~fixed.$

$The~production~function~is~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~Find~the~equation~of~the~isoquant~of~the~production~function,~given~the~value~of~Y~fixed.$

$The~production~function~is~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~Find~the~gradient~of~the~isoquant~of~the~production~function,\frac{dK}{dL}.~$

$The~production~function~is~Y=AL^{\frac{3}{4}}K^{\frac{1}{4}}.~Find~all~the~correct~arguments~about~the~isoquant~of~the~production~function.~The~y~axis~is~the~$$~level~of~capital~-~K,~and~the~x~axis~is~L.$
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