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1. Use the given Taylor polynomial p 2 to approximate the given quantity.
2. Compute the absolute error in the approximation assuming the exact value is given by a calculator.
Approximate e-0.07 using f(x) = e-x and p2(x) = 1 - x + x2/2

Respuesta :

zainsubhani

Answer:

Part 1:

P₂(0.07)=0.93245≈[tex]e^{-0.07}[/tex]

Part 2:

Error=[tex]0.5618*10^{-4}[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=e^{x}\\f(-0.07)=e^{-0.07}[/tex]

P₂(x)=[tex]1-x+\frac{x^2}{2}[/tex]

Solution:

Part 1:

P₂(x)=[tex]1-x+\frac{x^2}{2}[/tex]

We have x=0.07

Put Value of x in above Equation:

P₂(0.07)=[tex]1-0.07+\frac{0.07^2}{2}[/tex]

P₂(0.07)=0.93245≈[tex]e^{-0.07}[/tex]

Part 2:

[tex]e^{-0.07}[/tex]=0.93239382 (Calculated using Calculator)

Error=|[tex]e^{-0.07}[/tex]-P₂(0.07)|=|0.93239382-0.93245|=0.00005618

Error=|0.93239382-0.93245|

Error=0.00005618

Error=[tex]0.5618*10^{-4}[/tex]

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