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underset (xto0)lim(10^(x)-2^(x)-5^(x)+1)...

`underset (xto0)lim(10^(x)-2^(x)-5^(x)+1)/(l n (secx))` is equal to

A

`(l n2)(l n 10)`

B

`(l n 2)(l n 5)`

C

`(l n 4)(l n 5)`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto0)lim(10^(x)-2^(x)-5^(x)-1)/(l n (secx))=underset(xto0)lim(2^(x)(5^(x)-1)-(5^(x)-1))/(-l n (cosx))`
`underset(xto0)lim((2^(x)-1)(5^(x)-1))/(-l n (1+cosx+1))`
`=(-underset(xto0)lim((2^x-1)(5^(x)-1))/("x x"))/((ln(1+(cosx-1)))/((cosx-1)((cosx-1))/(x^(2))))=-((l n2)(l n 5))/(1xx-(1)/(2))`
`(l n4)(l n 5)`
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