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lim(x→inf.){sqrt[(x+a)(x+b)] - sqrt[(x-a)(x-b)]}
= lim(x→inf.)[(x+a)(x+b) - (x-a)(x-b)]/{sqrt[(x+a)(x+b)] + sqrt[(x-a)(x-b)]}
= 2(a+b)*lim(x→inf.)x/{sqrt[(x+a)(x+b)] + sqrt[(x-a)(x-b)]}
= 2(a+b)*lim(x→inf.)1/{sqrt[(1+a/x)(1+b/x)] + sqrt[(1-a/x)(1-b/x)]}
= a+b.
1年前
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