Proof of correctness Prove that 1 The loop will stop in a finite number of steps 2 The approximation y produced by the algorithm satsifies Algorithm 1 sin(x) via Taylor series Input r E IR E R20 Output an approximation y such that y Sin E Do y y ( 1) 1r2K 1 (2k 1) until 2k 1 (2k 1) E return y

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Question: Proof of correctness: Prove that: 1. The loop will stop in a finite number of steps. 2. The approximation y produced by the algorithm satsifies

Proof of correctness: Prove that: 1. The loop will stop in

Proof of correctness:

Prove that:

1. The loop will stop in a finite number of steps.

2. The approximation y produced by the algorithm satsifies a finite number of steps. 2. The approximation y produced by the

Algorithm 1 sin(x) via Taylor series Input: r E IR; E R20 Output: an approximation y such that y Sin E Do y y-- (-1) 1r2K-1/(2k -1)! until 2k-+1 /(2k 1)! E return y

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