3. (Laurent series expansions) Find the Laurent series expansions of the following functions in the regions indicated: z+1 (a) in 0 < 스프 ^ 8 (b) in 0 < |z – 4| < 4 z(z – 4)3
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- 2. (a) Find the Maclaurin series of 2/3+x^5 from the Maclaurin series for 1/1 - x and power series operations. (b) Use part (a) to calculate the definitie integral 1∫0 2/3+x^5dx. Please note the integral bounds are 1 and 0.8.7.4. Find the Maclaurin series (i.e., Taylor series about c = 0) and its interval of convergence.5. Using the Taylor series of e^x about x = 3, find the first three terms of Taylor series andthe error in terms of h for e^(3−2h)..