求lim(x->a+)(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2的极限
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求lim(x->a+)(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2的极限
求lim(x->a+)(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2的极限
求lim(x->a+)(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2的极限
lim(x->a+) 【x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2】
= lim(x->a+) 【(√x-√a) + √(x-a) / √(x^2-a^2)】
= lim(x->a+) 【(x-a)/(√x+√a) + 1 / √(x+a)】
= 0/(√a+√a) + 1/√(a+a)
= 1/√(2a) = √(2a) /(2a)
(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2
=(x^1/2-a^1/2)/(x^2-a^2)^1/2+(x-a)^1/2/(x^2-a^2)^1/2
=[(x^1/2-a^1/2)(x^1/2+a^1/2)]/[(x^1/2+a^1/2)*(x+a)^1/2*(x-a)^1/2]+(x-a)^1/2/[(x+a)^1/2*(x-a)^1/2]
=(x-a...
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(x1/2-a1/2+(x-a)1/2)/(x2-a2)1/2
=(x^1/2-a^1/2)/(x^2-a^2)^1/2+(x-a)^1/2/(x^2-a^2)^1/2
=[(x^1/2-a^1/2)(x^1/2+a^1/2)]/[(x^1/2+a^1/2)*(x+a)^1/2*(x-a)^1/2]+(x-a)^1/2/[(x+a)^1/2*(x-a)^1/2]
=(x-a)/[(x^1/2+a^1/2)*(x+a)^1/2*(x-a)^1/2]+1/(x+a)^1/2
=(x-a)^1/2/[(x^1/2+a^1/2)*(x+a)^1/2]+1/(x+a)^1/2
当x->a+时,(x-a)^1/2/[(x^1/2+a^1/2)*(x+a)^1/2]->0
1/(x+a)^1/2->1/(2a)^1/2
即所求的极限是根号2a分之1
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