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Let f(x) = x^-1/2. The first four derivatives of f(x) are f’(x) = -1/2x^-3/2, f’’(x) = 3/4 x^-5/2, f’’’(x) = -15/8x^-7/2, fiv(x) = 105/16x^-9/2. (a) Write down T3, the Taylor polynomial of degree 3 for f(x) centred at 4 . (b) Use Taylor's remainder theorem (Property 2.9) to give an upper bound on the error when using T3 to estimate 1/√2. [Hint: for part (b) you need to write down the formula for the error E3(x) and find an upper bound for this on the interval (2,4).]

Let f(x) = x^-1/2. The first four derivatives of f(x) are f’(x) = -1/2x^-3/2, f’’(x) = 3/4 x^-5/2, f’’’(x) = -15/8x^-7/2, fiv(x) = 105/16x^-9/2. (a) Write down T3, the Taylor polynomial of degree 3 for f(x) centred at 4 . (b) Use Taylor's remainder theorem (Property 2.9) to give an upper bound on the error when using T3 to estimate 1/√2. [Hint: for part (b) you need to write down the formula for the error E3(x) and find an upper bound for this on the interval (2,4).]

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Let f(x) = x^-1/2. The first four derivatives of f(x) are f’(x) = -1/2x^-3/2, f’’(x) = 3/4 x^-5/2, f’’’(x) = -15/8x^-7/2, fiv(x) = 105/16x^-9/2. (a) Write down T3, the Taylor polynomial of degree 3 for f(x) centred at 4 . (b) Use Taylor's remainder theorem (Property 2.9) to give an upper bound on the error when using T3 to estimate 1/√2. [Hint: for part (b) you need to write down the formula for the error E3(x) and find an upper bound for this on the interval (2,4).]

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