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What is  where a > b > 1, equal to?

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NDA 02/2021: Maths Previous Year paper (Held On 14 Nov 2021)
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  1. -1
  2. 0
  3. 1
  4. Limit does not exist

Answer (Detailed Solution Below)

Option 3 : 1
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Detailed Solution

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Given:

f(x) =  and

a > b > 1

Calculation:

We have,

a > b > 1

⇒  or 

Given that,

f(x) =     

⇒ f(x) =  

⇒ f(x) =  

Taking limit n→∞

⇒ f(x) =   

⇒ f(x) =        (∵  )

∴  f(x) = 1

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