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MTH301 Calculus II Assignment 1 Solution Spring 2019.


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MTH301 Calculus II Assignment 1 Solution Spring 2019.

Q1: Let 

h(x,\,y)\,\, = \,\,x\,y\,\,\, + \,x ,

        If  u(x,\,y)\,\, = \,\,{x^2}\,\,y{\,^3}  and v(x,\,y)\,\, = \,\,\frac{{x\,y}}{2}\,  , then find h(\,u,\,\,v\,).

{h\left( {x,y} \right){\rm{ }} = {\rm{ }}xy{\rm{ }} + {\rm{ }}x}

{h\left( {u,v} \right){\rm{ }} = {\rm{ }}uv{\rm{ }} + {\rm{ }}u{\rm{ }} \ldots .eq{\rm{ }}\left( 1 \right)}

Q2: Let f(x,\,y)\,\, = \,\,{x^5}\,\,Sin\,(\,x\,{y^2}\,) , then find partial derivatives of f(x,\,y) with respect to x and y at x\, = \,2,\,\,y\,\, = \,\,0             (Hint:  find \frac{\partial }{{\partial x}}f(2,\,0)   and \frac{\partial }{{\partial y}}f(2,\,0).)

 

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