MATH104 December 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q1 (o) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) •
Question 06 (d)
Consider the curve . Assume that the point (x,y) = (1,1) lies on the curve, and that nearby points on the curve satisfy y=f(x) for some function of f(x).
Write down the quadratic approximation of f(x) at x=1. Sketch its graph in the x,y grid below.
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Quadratic approximations are given by second degree Taylor polynomials which are given by
Compute this, then graph.
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Plugging in the values from part (a) and part (b) into the second degree Taylor polynomial (recalling the a value is 1) gives
The graph is given below.
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