Equation of the best quadratic approximation?

Rumor

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Sep 8, 2009
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I'm not sure what to do for this. Here's the problem:

"(a) Find the equation of the best quadratic approximation to y=ln(x) at x=1. The best quadratic approximation has the same first and second derivatives as y=ln(x) at x=1.

(b) Use a computer or calculator to graph the approximation and y=ln(x) on the same set of axes. What do you notice?

(c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

Parts b and c, I don't doubt that they'd be easy after getting part a.
So could someone help me with part a?
 
Rumor said:
I'm not sure what to do for this. Here's the problem:

"(a) Find the equation of the best quadratic approximation to y=ln(x) at x=1. The best quadratic approximation has the same first and second derivatives as y=ln(x) at x=1.

Start with generalized quadratic equation:

y = Ax[sup:2qydbsqt]2[/sup:2qydbsqt] + Bx + C

The differentiate - satisfy the required conditions and solve...


(b) Use a computer or calculator to graph the approximation and y=ln(x) on the same set of axes. What do you notice?

(c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

Parts b and c, I don't doubt that they'd be easy after getting part a.
So could someone help me with part a?
 
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