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Evaluate the given functions by using the series developed in the examples of this section.$$\sqrt{3.5}$$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 5

Taylor Series

Series

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Okay. So in this example we're asked to uh numerically approximate square root of 3.5 by using taylor series. So in the textbook, they say that the taylor series for squared of X is two plus x minus wine over four minus x minus one squared over 64 plus x minus one. You over 512. Close some additional terms. So essentially what we're gonna do is we're gonna put 3.5 in for X. So we're just going to put 3.5 in all of these exits here. So therefore we can say square root of 3.5 is equal to two plus 3.5 minus one over four minus 3.5 minus one, squared over 64 plus 3.5 minus one. Cubed over 512 plus additional terms. Okay, so after putting this in your calculator, we'll get to plus zero point 6 to 5 minus 0.0 976 plus 0.0 305 Okay, And after adding this together, we get two point 55 eight

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