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Evaluate lim(x->2)(x^(10)-1024)/(x^5-32)...

Evaluate `lim_(x->2)(x^(10)-1024)/(x^5-32)`

Text Solution

Verified by Experts

`underset(xto2)lim(x^(10)-1024)/(x^(5)-32)=underset(xto2)lim(x^(10)-2^(10))/(x^(5)-2^(5))=underset(xto2)lim((x^(10)-2^(10))/(x-2))/((x^(5)-2^(5))/(x-2))`
`=(underset(xto2)lim(x^(10)-2^(10))/(x-2))/(underset(xto2)lim(x^(5)-2^(5))/(x-2))=(10xx2^(10-1))/(5xx2^(5-1))`
`=64`
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