1. Find dz/dt for z= sin(x/y) where x=t, t=2t-1 2. Find the differential df from

ID: 3342440 • Letter: 1

Question

1. Find dz/dt for z= sin(x/y) where x=t, t=2t-1

2. Find the differential df from the gradient. grad f= (x+y)i+yj

3. Find the equation of the tangent plane to z=8/xy at the point (1,2,4)

4. Find the quadratic Taylor polynomial about (0,0) for f(x,y)= 1/(x+y+1). Approximate the value of (0.1,0.1)

5. Find the maximum value of f(x,y)= xy+1 on the triangular region x%u22650 , y%u22650, x+y%u22641

6.As open rectangular box has volume 100 cm^3. What are the lenghts of the edges giving the minimum surface area?

1) dz/dt = cos(x/y) * dx/dt * 1/dy/dt

=cos(t/(2t-1)) *t/2t

=cos(t/2t-1) * 1/2

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