Question

Question:
In this question, we are interested in finding x such that f(x) = 0, where f(x) = x − 𝑠in(x) − 0.01
i. Use the fact that 𝑠in(x) ≈ x− x3/3! to estimate when f(x) = 0.
ii. Apply two iteration of the Newton Raphson method to f(x) = 0. Use your estimate of the solution from part (i) as x^0. Do your calculation to at least four decimal places.
iii. Which other method you have studied can converge to the solution faster than Newton Raphson
Method? On what basis you think your suggested method (if any) converge faster ?

Answer 1

The 24 consonant sounds comprise six stops (plosives): p, b, t, d, k, g; the fricatives f, v, θ (as in thin), ð [eth] (as in then), s, z, ∫ [esh] (as in ship), Ʒ (as in pleasure), and h; two affricatives: t∫ (as in church) and dƷ (as the j in jam); the nasals m, n, ŋ (the sound that occurs at the end of words such as young); the lateral l; the postalveolar or retroflex r; and the semivowels j (often spelled y) and w. These remain fairly stable, but Inland Northern American differs from RP in two respects: (1) r following vowels is preserved in words such as door, flower, and harmony, whereas it is lost in RP; (2) t between vowels is voiced, so that metal and matter sound very much like British medal and madder, although the pronunciation of this t is softer and less aspirated, or breathy, than the d of British English.