Practice Problems: Taylor Polynomials (x=c)
Practice Questions
1. Find the Taylor polynomial of degree 3 for f (x) = cos x centered at c = π/3.
2. Find the Taylor polynomial of degree 4 for f (x) = ex centered at c = 1.
3. Find the Taylor polynomial of degree 3 for f (x) = ln(1 + x) centered at c = 0.5.
4. Approximate e0.2 using the degree 2 Taylor polynomial centered at c = 0.
5. Approximate sin(0.3) using the degree 3 Taylor polynomial centered at c = 0.
√
6. Find the Taylor polynomial of degree 3 for f (x) = 1 + x centered at c = 0.
7. Find the Taylor polynomial of degree 4 for f (x) = tan−1 (x) centered at c = 0.
8. Approximate cos(0.1) using the degree 2 Taylor polynomial centered at c = 0.
9. Find the Taylor polynomial of degree 3 for f (x) = e−x centered at c = 0.
10. Find the Taylor polynomial of degree 4 for f (x) = sin(2x) centered at c = 0.
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Practice Questions
1. Find the Taylor polynomial of degree 3 for f (x) = cos x centered at c = π/3.
2. Find the Taylor polynomial of degree 4 for f (x) = ex centered at c = 1.
3. Find the Taylor polynomial of degree 3 for f (x) = ln(1 + x) centered at c = 0.5.
4. Approximate e0.2 using the degree 2 Taylor polynomial centered at c = 0.
5. Approximate sin(0.3) using the degree 3 Taylor polynomial centered at c = 0.
√
6. Find the Taylor polynomial of degree 3 for f (x) = 1 + x centered at c = 0.
7. Find the Taylor polynomial of degree 4 for f (x) = tan−1 (x) centered at c = 0.
8. Approximate cos(0.1) using the degree 2 Taylor polynomial centered at c = 0.
9. Find the Taylor polynomial of degree 3 for f (x) = e−x centered at c = 0.
10. Find the Taylor polynomial of degree 4 for f (x) = sin(2x) centered at c = 0.
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