MATH200 December 2011
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 • Q5 (a) • Q5 (b) • Q6 • Q7 • Q8 (a) • Q8 (b) i • Q8 (b) ii • Q8 (b) iii •
Question 01 (c)
Consider the function
c) Find the tangent plane approximation to the value of using the tangent plane from part (b).
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The tangent plane you derived in part (b) should provide a good estimate for f(x,y) for values of (x,y) near (2,1). Simply plug in the values of (x,y) into your tangent plane approximation to estimate .
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From part (b), we found that the tangent plane to the surface at the point was
Since the point is very close to , the tangent plane approximation gives a good estimate for the true value of . Plugging in into the tangent plane equation we get
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Tangent plane