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We wish to compute [2 $2+3 dm. 2 m3 +4m2 16:c64 (i) We begin by factoring the denominator of the rational function. We get :53

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We wish to compute [2 $2+3 dm. 2 m3 +4m2 16:c64 (i) We begin by factoring the denominator of the rational function. We get :53 +432 16x64: (wa)(a:b)2 fora7b.Whatarea andb? FORMATTING: Make sure b corresponds to the factor of the denominator that repeats twice. a: Number , b: Number (ii) Next, we express the fraction in the form x2+3 A B 0 : + +. $3+4332163364 230, 335 (mb)2 Give the exact values of A , B and C . FORMATTING: Make sure A, B, and 0 correspond to the appropriate denominators, as given in the above setup. A: B: la 0: (iii) Finally, we use this partial fraction decomposition to compute the integral. Give its approximate value with 3 decimal places. 2 2 3 f L do a: Number 2 333 +4332 16:1: 64

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