Taylor series is 
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)
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.
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Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)
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Following the pattern, we can see that for 
,
This applies for n ≥ 1, Expressing f(x) in summation, we have
Combining ln2 with the rest of series, we have
Taylor series is
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Count change of signs to tell positive roots
then replace x with -x and evaluate, then count change in sign for negative roots
initially
+, -, -, +, +, -
3 changes
3 or 1 positive roots
replacing x with -x
-,-,+,+,-,-
2 changes
2 or 0 negative roots
B is answer
Answer:
a) 
b) 
c), Yes;
Step-by-step explanation:
Michael's Weight: 
Al's weight: 
a) Ratio of Michael's weight to Al's weight:
b) This ratio simplifies to: 
c) Yes, If the exponent in each expression were negative, then we have:
Ratio of Michael's weight to Al's weight: 
This ratio simplifies to: 
The two ratios are not the same.
