(a) Expand (1+px)-S p 0 in ascending powers of x, up to and including the term in x* Give each term in its simplest form. The coefficient of x' in the expansion is cr Given that c4 = 2c3 (b) find the value of p.

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Q: 41. Use the Taylor series generated by e* at x = a to show that (x – a)² e* = 1 + (x – a) + 2!

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Q: +00 (-1)" The Maclaurin series expansion of tan-1I is given by tan¬ I = (2n + 1) 2n+1 for r €…

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Q: 1 1 Express the series > + – 1 as a rational function. n=1 (x – 6)2n- (æ – 3)²r 2n – 1 -

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Q: (a) Show that the p.d.f. of Zf is given by g1(r) = e-(+)cosh(vAr), z > 0, where cosh(2) = (e +e) is…

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Q: 1. Determine whether the function is even, odd, or neither: x + 5, -2 <x <0 -x + 5, f (x) = 0 <x < 2…

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Q: Q./ Prove( in detail) the solution of (bn) in fourier series is ( -4n / n)

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Q: 29-30 The limit of an indeterminate form as xXo can some- times be found by expanding the functions…

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Q: (-1)"x²n = E-0 x" and cos x = 0 100 For #6, given that find a power series 1-x (2n)! representation…

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