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- . Show that the estimate and the estimation error for an MMSE estimator are orthogonal (Hint: X and Y are orthogonal if E[XY ] = 0).Verify the given linear approximation at a=0 . Thendetermine the values of x for which the linear approximation isaccurate to within 0.1.Given the linear approximation at a=0, determine the smallest value x of such that the linear approximation is accurate to within 0.1.
- Let y = 4x^2 + 8x + 2. If delta x=0.4 at x=5, use linear approximation to estimate delta y. Delta y= ?Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy.Δy≈ ?Find the equation of the tangent line and equation of the normal line to the graph of3x cos y = 1 + x^2 +√ 2y + 1 at P(1, 0).
- What is the difference between the linearization, L(x), of f at a, and the linear approximation (or tangent line approximation), f(x) ≈ L(x), of f at a?Find the normal line to f(x)=ax^2-3ax at x=2. Assume that a is a positive constant.A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show that (b) Estimate the percentage increase in V if r and h are each increasedby 2%.