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- 13 By considering the Maclaurin expansions of sin(kx) and cos (kx), k constant, evaluate if possible sin(kx) (a) lim cos (kx) – 1 (b) lim sin(kx) (c) lim X→0 1 – cos (kx)it is shown that the number of multiplication needed to compute x100 is 8. Using the same method, how many multiplications are needed to compute x111?1 2 1 5. Prove that 3 . Hint: Compute e-' from the continued frac- 1 1 + 2 + 3 + … tion for e given in the text.
- Suppose it is known that the coefficients in the expansion and express this in terms of familiar elementary functions. f(x) = anx" n=0 satisfy (n + 2)an+1x" -anx" = 0. n=0 n=0 Show that ao f(x) = 1 "+1 (n + 1)! n=0(a) Express (4-3x)ž in the form of a(1+ bx)ž where a and be R. Hence, 3 find the expansion of (4–3x)ž up to the term in x'. (b) By substituting x=- into (4-3x) and the expansion, evaluate 33 correct to two decimal places.5. Expand the following function in Fourier series where f(x) = { show that f(x): = + 22-1 [(-1)^-1 nπ ·cos nxX- [1 when -1- Find the Fourier series expansion of the given function, whose definition in one period as: (24) f(x)=cosx (25) f(x) = sinx | (26)f(x)=x| (27) f(x) = sin(tx) 三 (28) f(x)=x3 (29) f (t)= (30) f ( )= sint 一π n-t1) How many integers are there in the domain of the function f(x) = In (x? – x - 12) + v25 – x? + sin-1 (x+ 4) ?Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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