极限
1 原式=(求导)lim(x趋向2)cos(x-2)/(2x)=1/4 1 原式=lim(x趋向2)(sin(x-2) /(x-2)) / (x+2) =lim(x趋向2)1/ (x+2)=1/4 2 原式= lim(x趋向无穷大)(1-3/x)^(-x/3)^(-3) = e^(-3)
(1)sin(x-2)/(x^2-4)=[sin(x-2)/(x-2)]*[1/(x+1)], ∴原式=lim(x—>2)sin(x-2)/(x-2)]*lim(x—>2)[1/(x+1)]=1*1/3 =1/3. (2)(1-3/x)^x=[(1-3/x)^(-x/3)]^(-3),(1-3/x)^(-x/3)—>e, ∴原式=1/e^3.
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