What values of x should be used in the sequence to approximate f(x)=3^√2 to three decimal places?(1 point) Responses 1, 1.4, 1.41, 1.414, 1.4142, 1.41421, 1.414213 1, 1.4, 1.41, 1.414, 1.4142, 1.41421, 1.414213 1, 1.4, 1.41, 1.414, 1.4142, 1.41421 1, 1.4, 1.41, 1.414, 1.4142, 1.41421 1, 1.4, 1.41, 1.414, 1.4142 1, 1.4, 1.41, 1.414, 1.4142 1, 1.4, 1.41, 1.414

1 answer

To approximate \( f(x) = 3^{\sqrt{2}} \) to three decimal places, you want to choose a value of \( x \) that will yield \( \sqrt{2} \) closely, as \( f(x) = 3^{\sqrt{2}} \).

The values given for \( x \) are approximations of \( \sqrt{2} \):

  • \( 1 \)
  • \( 1.4 \)
  • \( 1.41 \)
  • \( 1.414 \)
  • \( 1.4142 \)
  • \( 1.41421 \)
  • \( 1.414213 \)

Among these, the value \( 1.414213 \) is the most accurate approximation of \( \sqrt{2} \) (which is approximately \( 1.41421356 \ldots \)).

To find \( f(x) = 3^{\sqrt{2}} \), you can use \( x = 1.414213 \). This would give you the closest approximation of \( f(x) \) to three decimal places.

Thus, you should use 1.414213 for your sequence to approximate \( f(x) = 3^{\sqrt{2}} \) to three decimal places.