lim X--> 0((x+2)^1/3 - (2)^1/3)/x

Dear Student,
Please find below the solution to the asked query:

We have:L=limx0 x+213-213x=limx0 x+213-213xx+223+223+x+213.213x+223+223+x+213.213We know that:a-ba2+b2+ab=a3-b3, hence we get:L=limx0 x+233-233x1x+223+223+x+213.213=limx0 x+2-2x1x+223+223+x+213.213=limx0 xx1x+223+223+x+213.213=limx0 1x+223+223+x+213.213Applying limit, we get:L= 1223+223+213.213=1223+223+223=13223limx0 x+213-213x=13223

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