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#6 FRQ AP CALC BC 2022 Part 2

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#6 FRQ AP CALC BC 2022 Part 2
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  • 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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