(All Steps) Use Newton's divided differences set out in tabular form as in notes to find a quadratic approximation for e^x using x=0,1,2, and use this to

Question: Use Newton's divided differences set out in tabular form as in notes to

find a quadratic approximation for $\mathrm{e}^{\mathrm{x}}$ using $\mathrm{x}=0,1,2$, and use this to find an approximation for $\mathrm{e}^{\mathrm{x}}$ at $\mathrm{x}=1.5$
extend this approximation to a cubic using $\mathrm{x}=3$, and use this to find an approximation for $\mathrm{e}^{\mathrm{x}}$ at $\mathrm{x}=1.5$
compare the above approximations with the value of $\mathrm{e}^{\mathrm{x}}$ at $\mathrm{x}=1.5$.

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(All Steps) Use Newton's divided differences set out in tabular form as in notes to find a quadratic approximation for e^x using x=0,1,2, and use this to

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