Question:

1. Let \(f\left( x,y \right)={{x}^{3}}+x{{y}^{2}}-2y\). Use the chain rule to find the rate of change of \(f\left( x,y \right)\), \(\frac{df}{dt}\) along the parametric curve \(x\left( t \right)={{t}^{3}}\), \(y\left( t \right)=2{{t}^{2}}\) at the time t = 1.
2. Let \(f\left( x,y \right)=xy-{{x}^{3}}\)
   Obtain the Taylor series of the function \(f\left( x,y \right)\) about the point ( x , y ) = (1,1). Neglect terms of degree three and higher. Write your answer as a function of and \(\Delta x\) and \(\Delta y\)
3. Find the point on the plane \(2x+y-z=6\) which is closest to the origin by using Lagrange multipliers.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document