高等数学 极限.两小题（简单）1对不起对不起 第一题我打错了lim[(x+a)/(x-a)]^x

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1：= lim{[1+2a/(x-a)]^(x-a)/2a}^[2ax/(x-a)]
= {lim[1+2a/(x-a)]^(x-a)/2a}^lim[2ax/(x-a)]
= e^2a2:= lim [(5+1/x^2)/(3-1/x)]*[sin(1/x)/(1/x)]
= lim[(5+1/x^2)/(3-1/x)] * lim[sin(1/x)/(1/x)]
= 5/3 * 1
= 5/3======以下答案可供参考======
供参考答案1:
1) lim(x+a)/(x-a)=lim(1+a/x)/(1-a/x)=1
x->∞ x->∞2)因为x->∞时,sin1/x1/x
所以 原式=lim(5x^2+1)*1/x/(3x-1)
x->∞ =lim(5+1/x^2)/(3-1/x)
x->∞ =5/3供参考答案2:
1（x+a)/(x-a)
=(x-a+2a)/(x-a)
=1+2a/(x-a)
=12(5x^2 + 1)/(3x-1) * sin(1/x)
=(5x+1/x)/(3-1/x)*sin(1/x)
=5x/3*sin(1/x)
=5/3*sin(1/x)/(1/x)
=5/3