1. Let r(t) = (2 cos(t), 2 sin(t), t). (a) Computer (b) Computer (c) Find the unit tangent vector T. (d) Find the normal vector N. (e) Find the binormal vector B. (f) Find the curvature. (g) Find the acceleration. (h) Find the normal component of the acceleration. (i) Find the tangential component of the acceleration. 2. Compute lim 2xy if it exists. (x, y)-(0,0) x2+y2 3. Compute lim X (x, y) -(0,0) x2 +yz if it exists. 4. Let f(x,y)=ax2 +bxy+cy2. Compute (a) fx ( b ) fy (c) fxx (d) fxy (e) fyy 5. Let f(x, y) = e-x2-y. Compute (a) fx (b) fy (c) fxx (d) fxy (e) fyy 6. Write the equation of the tangent plane to z = x2+4xy+4y at the point (x, y) = (1, 1). 7. Write the linear approximation of f (x, y) = x2 + 4xy + 4y2 at the point (x, y) = (1, 1). 8. If z = x2 + 4xy + 4y2, express the differential dz in terms of dx and dy