Use the following approximation
${(1 + x^{2})}^{- 3} \approx 1 - 3 x^{2} + 6 x^{4} - 10 x^{6} + 15 x^{8} - 21 x^{10}$
to estimate ${(\frac{16}{17})}^{3}$ . Round the answer to three decimal places.

Answer

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Answer

Final Answer: The approximation of ${(\frac{16}{17})}^{3}$ is $1.199$ .

Steps

Step 1 ：Rewrite ${(\frac{16}{17})}^{3}$ as ${(1 - \frac{1}{17})}^{3}$ , which is in the form of ${(1 + x^{2})}^{- 3}$ where $x^{2} = - \frac{1}{17}$ .

Step 2 ：Substitute $x^{2}$ into the approximation and calculate the result.

Step 3 ： $x^{2} = - 0.058823529411764705$

Step 4 ：approximation = 1.199461635925308

Step 5 ：Final Answer: The approximation of ${(\frac{16}{17})}^{3}$ is $1.199$ .

Use the following approximation(1+x2)−3≈1−3x2+6x4−10x6+15x8−21x10to estimate (1617)3. Round the answer to three decimal places.

Answer

Popular Problems

Use the following approximation
${(1 + x^{2})}^{- 3} \approx 1 - 3 x^{2} + 6 x^{4} - 10 x^{6} + 15 x^{8} - 21 x^{10}$
to estimate ${(\frac{16}{17})}^{3}$ . Round the answer to three decimal places.