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- Consider z = z (x, y) Find (∂z / ∂x )and (∂z / ∂y )by implicit derivation and confirm that the result obtainedDetermine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = x √y for (x,y) near the point (1,4).Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = tan−1 (x + 2y) for (x,y) near the point (1,0).
- Use Euler method to approximate the value of y(0.1), given y' - x2 - y = 5 , y(0) = 2 with Δx = 0.025if z=f(x,y)=x^4-3xy+1 and x=2t, y=t^3 find dzdt using the chain ruleIf w = ln (x2 + y2 + 2z), x = r + s, y = r - s, and z = 2rs, find w r and w s by the Chain Rule. Then check your answer another way.
- (a) express ∂z/∂u and ∂z/∂y as functions of uand y both by using the Chain Rule and by expressing z directly interms of u and y before differentiating. Then (b) evaluate ∂z/∂u and∂z/∂y at the given point (u, y). z = 4ex ln y, x = ln (u cos y), y = u sin y;(u, y) = (2,π/4)Determine the 2nd degree Taylor polynomials Q(x, y) for f(x, y) = ln(x^2 +y^2 + 1) for (x, y) near the point (0, 0).Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s − 3t.
- Using the chain rule, find df/dt in terms of t if, f(x,y)=xsin(y) and x = 5*t, y = t^2How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization to estimate g(1.08, 1.037). thank you.Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.