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Find the following limits : lim(xrarr1...

Find the following limits :
`lim_(xrarr1) {(x^(1/5)-1)/(x^(1/100)-1)}`

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`lim_(xrarr1) {(x^(1/5)-1)/(x^(1/100)-1)}`
Let ``x^(1/100)= t implies x^(1/5)= t^20` and as `x rarr 1 implies t rarr 1`
Then `lim_(xrarr1){(x^(1/5)-1)/(x^(1/100)-1)}`
`= lim_(xrarr1){(t^20-1)/(t-1)} = 20.1^(20-1)=20`
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