1. |x| < 16 |x| < 12 |x| < 1 |x| < 6
Use the binomial series to expand the function as a power series. Find the radius of convergence. {image}
|x| < 16
|x| < 12
|x| < 1
|x| < 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. |x| < 13 |x| < 1 |x| < 10 |x| < 5
Use the binomial series to expand the function as a power series. Find the radius of convergence. {image}
|x| < 13
|x| < 1
|x| < 10
|x| < 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Use the binomial series to expand {image}1.
{image} 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Expand {image} as a binomial series.1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. The period of a pendulum with length L that makes a maximum angle {image} with the vertical is {image} where {image} and g is the acceleration due to gravity. Use the inequality {image} to estimate to the thousandth the period of a pendulum with L = 2 meter, {image} and g = 9.8.
T = 3.825
T = 2.092
T = 2.846
T = 3.479
T = 2.251
T = 3.821 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50