To identify how much heat is required to bring a kettle of water to its boiling point, you are required to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table Q1(a). Q1 _(a) Table Q1(a): Specific heat of water as a function of temperature Temperature, T Specific heat, C, (C) J kg-°C) 42 4179 52 4186 82 4199 100 4217 110 4300 (i) Determine the value of the specific heat at T = 61°C using a second order Lagrange polynomial. (ii) Determine the value of the specific heat at T = 61°C using a third order Lagrange polynomial. Find the absolute relative approximate error e. obtained between the results from the second with third order polynomial. (iii)

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