FIND THE ANSWERS

Taylor's Theorem: Calc ll help please!?

Answer this question

  • Taylor's Theorem: Calc ll help please!?


Answers

Answer #1 | 23/07 2014 17:55
The problem is stating (in so many words) that you'll be approximating the error based on the specifically given terms of the Taylor [polynomial] series for cos(x) This means you'll need to find the next term in the Taylor series for cos(x) to find the error. Taylor series for cos(x) (normally found in the front/back of your textbook)... cos(x) = 1 - (x^2/2) + (x^4/24) ... (keeps going and going, but we only needed the next term in the series, which we can see, here, is [x^4/24]) Now, we'll find the max magnitude of error (absolute value of error) using our newly discovered term from the Taylor series with our given interval [-π/4 , π/4] |Error| = |x^4 / 24| Substitute: |Error| = |(π/4)^4 / 24| Simplify: |Error| = |(π^4/256) / 24| |Error| = |π^4/6144| |Error| = π^4/6144 |Error| = 0.015854344 Answer: 0.015854344 Hope it helps!
Answer #2 | 24/07 2014 00:55
The problem is stating (in so many words) that you'll be approximating the error based on the specifically given terms of the Taylor [polynomial] series for cos(x) This means you'll need to find the next term in the Taylor series for cos(x) to find the error. Taylor series for cos(x) (normally found in the front/back of your textbook)... cos(x) = 1 - (x^2/2) + (x^4/24) ... (keeps going and going, but we only needed the next term in the series, which we can see, here, is [x^4/24]) Now, we'll find the max magnitude of error (absolute value of error) using our newly discovered term from the Taylor series with our given interval [-π/4 , π/4] |Error| = |x^4 / 24| Substitute: |Error| = |(π/4)^4 / 24| Simplify: |Error| = |(π^4/256) / 24| |Error| = |π^4/6144| |Error| = π^4/6144 |Error| = 0.015854344 Answer: 0.015854344 Hope it helps!

Possible answer