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23 Nov 2019
Using Taylorâs theorem, compute the first four non-zero terms ofthe following functions. Keep the factorial terms in yourexpansions; do not simplify:
1. Expand f (x) = sin(x + p) about x = 0.
2. Expand f (x) = ln(x) about x = 1.
3. Expand f (x) = e^(x^2) about x = 0.
Using your result from 3, answer the following questions:
4. What is the truncation error of f (x) = e^(x^2)?
5. Compute the integral g(x) = (integral from 0 to 1of...)e^(x^2)dx using your Taylor expansion.
6. What is the truncation error of g(x)?
Using Taylorâs theorem, compute the first four non-zero terms ofthe following functions. Keep the factorial terms in yourexpansions; do not simplify:
1. Expand f (x) = sin(x + p) about x = 0.
2. Expand f (x) = ln(x) about x = 1.
3. Expand f (x) = e^(x^2) about x = 0.
Using your result from 3, answer the following questions:
4. What is the truncation error of f (x) = e^(x^2)?
5. Compute the integral g(x) = (integral from 0 to 1of...)e^(x^2)dx using your Taylor expansion.
6. What is the truncation error of g(x)?
