Suppose that a surface S is parametrized by the equationr(s,t)=<x(s,t),y(s,t),z(s,t)>[r is a vector valued function] where x(s,t) =es2t, y(s,t) = t-2s, z(s,t) = sin(t).

(a) Find the equation of the tangent plane to the surface at the point with (s,t) = (1,0).

(b) Now, using the information above and with new information, suppose that a function f(x,y,z) is defined in all ofR3, but we are specifically interested in its values on the surface S. Let us say for a new equation g(s,t) that g(s,t) = f(r(t)) = f(x(s,t),y(s,t),z(s,t)). Let's suppose that we know that f(1,-2,0) = 3,fx(1,-2,0) = -1,fy(1,-2,0) = 0,fz(1,-2,0) = 5 . Now, use the information given and use linear approximation to estimate g(1.01, -0.2).