Power Series & Taylor/Maclaurin Series (Calculus II)
Free printable university Calculus II worksheet on power series: finding the radius and interval of convergence with the ratio test, plus Maclaurin series for e^x, sin x and cos x and polynomial approximation.
✓ Answer key checked by math, never wrong
Calculus II · Math worksheet
Name
Date
Math
Calculus II: Power Series & Taylor/Maclaurin Series
Use the ratio test to find each power series' radius of convergence, then test both endpoints to give the interval. For the Maclaurin questions, write the series from the derivative pattern and use its partial sums to approximate function values.
- 1.Find the radius and interval of convergence of the power series Σ[n=1 to ∞] /(·n).
- 2.Find the radius and interval of convergence of the power series Σ[n=1 to ∞] /.
- 3.Find the radius and interval of convergence of the power series Σ[n=1 to ∞] /(·).
- 4.Find the radius and interval of convergence of the power series Σ[n=1 to ∞] /n!.
- 5.Find the radius and interval of convergence of the power series Σ[n=1 to ∞] n!·.
- 6.Write the first four nonzero terms of the Maclaurin series for f(x) = , and state the general term.
- 7.Write the first four nonzero terms of the Maclaurin series for f(x) = sin x, and state the general term.
- 8.Write the first four nonzero terms of the Maclaurin series for f(x) = cos x, and state the general term.
- 9.Use the first four nonzero terms of the Maclaurin series for (up to degree 3) to approximate . Round to 5 decimal places.
- 10.Use the first four nonzero terms of the Maclaurin series for sin x (up to degree 7) to approximate sin(0.5). Round to 5 decimal places.
- 11.Use the first four nonzero terms of the Maclaurin series for cos x (up to degree 6) to approximate cos(0.2). Round to 5 decimal places.
Made with ChalkBee · chalkbee.com