#6 FRQ AP CALC BC 2022 Part 2
Storyboard Text
- 7
- Write the first four nonzero terms and the general term for an infinite series that represents f'(x).
- This is part C of the free response question.
- How do we answer this question???
- 8
- f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n
- Just take the derivative of the given power series!
- 9
- Use the result from part (c) to find the value of f'(1/6).
- This is part D of the free response question (the final part)!!
- How do we answer this question???
- 10
- f'(x) = 1/(1-(-x^2) = f'(x) = 1/(1+x^2)
- f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n + ...
- f'(1/6) = 1/(1+(1/6)^2) = 36/37
- Since the infinite series for f'(x) is a geometric series, we can apply the geometric series formula!
- 11
- f'(x) = 1/(1-(-x^2) = f'(x) = 1/(1+x^2)
- f'(x) = 1 - x^2 + x^4 - x^6 + ... + (-1)^n*x^2n + ...
- f'(1/6) = 1/(1+(1/6)^2) = 36/37
- Any other questions??
- Where is Mr. T???
- 12
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