ap calculus bc review for quiz -determining convergence of geometric series -creating a power series...
TRANSCRIPT
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AP Calculus BC
Review for Quiz- Determining convergence of geometric series
- Creating a power series- Finding a Taylor Series sum expression
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Question 1
For the series below: Write the first 4 terms of the series, then find the sum that the series converges to.
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Solution Q1
1. 5 + 5/4 + 5/16 + 5/64 converges to 20/3
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Question 2
Find the power series expression for
Then use your result to find a power series representation for
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Solution Q2
And
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Question 3
Determine the fourth order Taylor series and the summation equation for f(x) = 1/x when the center is at x = -1
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Solution Q3
= - 1 – (x+1) - -
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Question 4
• Tell whether each converges or diverges, if it converges give its sum
a.b. + . . . . .
c. x - + - + . . . .
∑𝑛=1
∞
3( 12 )𝑛−1
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Q4 key
a. Converges to 6b. Converges to 2/3 (r = -1/2)c. Divergesd. Sin x
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Question 5
Find the interval of convergence and the function of x represented by the geometric series
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Q5 key
• The interval of convergence is – 1 < x < 3
• And f(x) =
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Question 6
Find the interval of convergence and the function of x represented by the geometric series
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Q6 key
• f(x) =
• And interval of convergence is (1,5)
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Question 7
Find first four terms of the Taylor polynomial for y =
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Q7 key
= 1 + (2x) +
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Question 8
Find the 5th partial sum and also what the series converges to.
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Q8 Key
5th partial sum is
= = 13.02469
Converges to: 15