4.求授限细蛊器 解：因为my一0-粤=1，所以 整3=3w2 一器-罩器提等 5.求四1+5cotj2a 餐：因为卿1+)i=6吗50ot工=5吗otx=0,所以 (om(co) ={+5点}”=e 6.求函数f(c)=sim(sinx)的一阶导数与二阶导数 f(r)=cos(sin r)cosr,f"(r)=-sin(sinr)cos2x-cos(sin r)sinr 数学分析（山）试题第4页（共8页） 4. ¶4Å limx→0− sin 3x sin 2x ): œè limy→0− sin y y = 1, §± limx→0− sin 3x sin 2x = limx→0− sin 3x 3x sin 2x 2x 3x 2x = 3 2 limx→0− sin 3x 3x limx→0− sin 2x 2x = 3 2 × 1 1 = 3 2 5. ¶ lim x→π 2 (1 + 5 cot x) 2 tan x . â: œè lim y→0 (1 + y) 1 y = e, lim x→π 2 5 cot x = 5 lim x→π 2 cot x = 0, §± lim x→π 2 n (1 + 5 cot x) 1 5 cot x o5 cot x×2 tan x = lim x→π 2 n (1 + 5 cot x) 1 5 cot x o10 =  lim x→π 2 (1 + 5 cot x) 1 5 cot x 10 = e 10 6. ¶ºÍ f(x) = sin(sin x) òÍÜÍ. â: f 0 (x) = cos(sin x) cos x, f00(x) = − sin(sin x) cos2 x − cos(sin x) sin x ÍÆ©¤ (II) £K 1 4 ê£
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