201-2015学年米一学湘《区文西与积分状一2 3sa园= 4.(1)(%)Evaluate the integral (1)(7%)Find the first two nonzero terms in the Taylor expansion of fz)around0. (2)(7%)Find the first two nonzero terms in the Laurent expansion of fz)around 1. (3)(6%)Does the limit f包 exi过？Prove your conclusion. (2)(10%)Find the Fourier transform of 00=x2+x+52014-2015 学年第一学期《复变函数与积分变换》期终考试试卷--2 3. Set f(z) = 𝑒 𝑧−1 𝑧(1−𝑧) (1) (7%) Find the first two nonzero terms in the Taylor expansion of f(z) around 0. (2) (7%) Find the first two nonzero terms in the Laurent expansion of f(z) around 1. (3) (6%) Does the limit lim𝑧→∞ 𝑓(𝑧) exist? Prove your conclusion. 4.(1) (10%)Evaluate the integral ∫ 𝑑𝑧 z 2sin𝑧 |𝑧|=4 (2) (10%)Find the Fourier transform of f(x) = 1 x 2 + 4𝑥 + 5