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Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2...

Let `p=lim_(x->0^+)(1+tan^2 sqrt(x))^(1/(2x))` then log p is equal to`

Text Solution

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`p=lim_(x->0^+)(1+tan^2sqrtx)^(1/(2x))`
`p=e^(lim_(x->0+))1/(2x)(x+tan^2sqrtx-x)`
`=e^(lim_(x->0^+)1/2tan^2sqrtx)/sqrtx^2`
`=e^(lim_(x->0^+)(1/2(tansqrtx)/sqrtx)^2`
`p=e^(1/2)`
`logp=log(e^(1/2))=1/2loge`
`logp=1/2`.
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