Values for f(x) = e-ª – 1+x are given in table. 1.2 1.4 f(x) | 0.25 | 0.37 | 0.5 | 0.65 0.8 1 a) Use forward-difference and backward-difference formulas to approximate f'(1)

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Chapter2: Second-order Linear Odes
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Values for f(x) = e¨ Р1 + x are given in table.
0.8
1
1.2
1.4
f(x) | 0.25
0.37
0.5 0.65
a) Use forward-difference and backward-difference formulas to approximate
f'(1)
b) Use three-point formulas to approximate f'(1) and find error bounds for
the three-point midpoint formula.
2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate
f"(1) when h = 0.2.
Transcribed Image Text:Values for f(x) = e¬® – 1 + x are given in table. 0.8 1 1.2 1.4 f(x) | 0.25 0.37 0.5 0.65 a) Use forward-difference and backward-difference formulas to approximate f'(1) b) Use three-point formulas to approximate f'(1) and find error bounds for the three-point midpoint formula. 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2.
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