Question

1. Use the given Taylor polynomial p 2 to approximate the given quantity.

Answer 1

Answer:

Part 1:

P₂(0.07)=0.93245≈$e^{-0.07}$

Part 2:

Error=$0.5618*10^{-4}$

Step-by-step explanation:

Given:

$f(x)=e^{x}\\f(-0.07)=e^{-0.07}$

P₂(x)=$1-x+\frac{x^2}{2}$

Solution:

Part 1:

P₂(x)=$1-x+\frac{x^2}{2}$

We have x=0.07

Put Value of x in above Equation:

P₂(0.07)=$1-0.07+\frac{0.07^2}{2}$

P₂(0.07)=0.93245≈$e^{-0.07}$

Part 2:

$e^{-0.07}$=0.93239382 (Calculated using Calculator)

Error=|$e^{-0.07}$-P₂(0.07)|=|0.93239382-0.93245|=0.00005618

Error=|0.93239382-0.93245|

Error=0.00005618

Error=$0.5618*10^{-4}$