Let z(x, y) Calculate дz მs дz 2t = дz მs & 7х2 + y² where x = s + 8t & y = дz St by first finding ?х ду дх 3 ?s' is t 1 & - 78 + 9t. ду St and using the chain rule.
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- Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.Sketch the slope field for y’ + y = 2 at the 25 gridpoints (x, y), where x = 0, 1, ... ,4 and y = 0, 1, ... ,4.Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by W(f1,f2)=e2xW(f1,f2)=e2x. Are the functions that you found linearly independent on (−∞,∞)(−∞,∞)? How do you know?
- Find the linearization of y=√x at a=49. Then use your linearization to approximate √56. Show workif z=f(x,y)=x^4-3xy+1 and x=2t, y=t^3 find dzdt using the chain ruleFind the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01, 1.02) and f(l.97, 1.01), and compare with values obtained using a calculator.
- express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)=− 2/3 ,2.Is the linear operator T : R3 --> R3 defined by T (x, y, z) = (2x - 3y + 7z, 5y + z, -z) diagonalizable?The linear operator T: R2 --> R2 defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?