来源:蜘蛛抓取(WebSpider)
时间:2023-06-15 13:29
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{@each tagList as item}
${item.tagName}
{@/each}
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x->0分子(sinx)^2 = x^2 +o(x^2)e^x = 1+ x +(1/2)x^2 +o(x^2)(sinx)^2 +e^x = 1+ x +(3/2)x^2 +o(x^2)ln[(sinx)^2 + e^x]=ln[1+ x +(3/2)x^2 +o(x^2)]=[x +(3/2)x^2] -(1/2)[x +(3/2)x^2]^2 +o(x^2)=[x +(3/2)x^2] -(1/2)[x^2 +o(x^2)] +o(x^2)=x + x^2 +o(x^2)ln[(sinx)^2 + e^x] -x = x^2 +o(x^2)分母e^(2x) = 1+ 2x + 2x^2 +o(x^2)(sinx)^2 + e^x = 1+ 2x + 3x^2 +o(x^2)ln[x^2+e^(2x)]=ln[1+ 2x + 3x^2 +o(x^2)]=[2x + 3x^2 ] -(1/2)[2x + 3x^2 ]^2 +o(x^2)=[2x + 3x^2 ] -(1/2)[4x^2+o(x^2)] +o(x^2)=2x + x^2 +o(x^2)ln[x^2+e^(2x)] -2x = x^2 +o(x^2)/lim(x->0) {ln[ (sinx)^2 + e^x ] -x }/{ ln[x^2+e^(2x)] -2x }=lim(x->0) x^2/x^2=1
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