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If agt0, b gt0 than lim(nrarroo) ((a-1+b...

If `agt0, b gt0` than `lim_(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=`

A

`b^((1)/(a))`

B

`a^((1)/(b))`

C

`a^(b)`

D

`b^(a)`

Text Solution

Verified by Experts

The correct Answer is:
A
`L=underset(nrarroo)(lim)((a-1+b^(x))/(a))^((1)/(x))`
`"Let "(1)/(n)=x,`
`therefore" "L=underset(xrarr0)(lim)((a-1+b^(x))/(a))^((1)/(x))`
`" "=e^(underset(xrarr0)(lim)((a-1+b^(x))/(a)-1)(1)/(x))`
`" "=e^(underset(xrarr0)(lim)((b^(x)-1)/(ax)))`
`" "=e^((1)/(a)log_(e)b)=b^((1)/(a))`
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CENGAGE-LIMITS-Single Correct Answer Type
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