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Evaluate the following lim(xto2)(x^3-8)/...

Evaluate the following `lim_(xto2)(x^3-8)/(x^5-32)`

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`lim_(xto2)(x^3-8)/(x^5-32)=lim_(xto2)(x^3-2^3)/(x^5-2^5)`
`lim_(xto2)((x^3-2^3)/(x-2))/((x^5-2^5)/(x-2))=(lim_(xto2)(x^3-2^3)/(x-2))/(lim_(xto2)(x^5-2^5)/(x-2))`
`=(3xx2^2)/(5xx2^4)=3/20 [thereforelim_(xtoa)(x^n-a^n)/(x-a)=na^(n-1)`
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