Question

Question 01: Find \( f^{\prime}(1.40) \) and \( f^{\prime \prime}(1.40) \) by using Newton's Backward difference formula for derivatives from the following table \begin{tabular}{|l|l|l|l|l|l|} \hline\( x \) & 1.24 & 1.28 & 1.32 & 1.36 & 1.40 \\ \hline\( f(x) \) & 3.2542 & 4.1562 & 4.8531 & 5.4623 & 6.1811 \\ \hline \end{tabular} Question 02: Using Simpson's \( 1 / 3 \) Rule to evaluate \[ \int_{0}^{12}\left(e^{-3 x}+0.5\right) d x \] (Divide the interval of integration into 8 equal parts.)

          Question 01:
Find \( f^{\prime}(1.40) \) and \( f^{\prime \prime}(1.40) \) by using Newton's Backward difference formula for derivatives from the following table
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( x \) & 1.24 & 1.28 & 1.32 & 1.36 & 1.40 \\
\hline\( f(x) \) & 3.2542 & 4.1562 & 4.8531 & 5.4623 & 6.1811 \\
\hline
\end{tabular}

Question 02:
Using Simpson's \( 1 / 3 \) Rule to evaluate
\[
\int_{0}^{12}\left(e^{-3 x}+0.5\right) d x
\]
(Divide the interval of integration into 8 equal parts.)

Question 01:
Find f^'(1.40) and f^''(1.40) by using Newton's Backward difference formula for derivatives from the following table

x 1.24 1.28 1.32 1.36 1.40

f(x) 3.2542 4.1562 4.8531 5.4623 6.1811

Question 02:
Using Simpson's 1 / 3 Rule to evaluate

∫0^12(e^-3 x+0.5) d x

(Divide the interval of integration into 8 equal parts.)

Added by Rebecca H.

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