1.

The value of Lim_(xto0) (5x^(2)+[x^(2)+1])^(((1)/(x^(2)+sin^(2)x))) is, [Note : [y] denotes greatest interger less than or equal to y.]

Answer»

`(5)/(2)`
`e^((5)/(2))`
`(25)/(2)`
`e^((25)/(2))`

Solution :`underset(xto0)LIM(5x^(2)+[x^(2)+1])^(((1)/(x^(2)+SIN^(2)x)))=e^(L)`
where `L=underset(xto0)Lim(1)/(x^(2)+sin^(2)x)(5x^(2)+[x^(2)+1]-1)=underset(xto0)Lim(5x^(2))/(x^(2)+sin^(2)x)=(5)/(2)`
`:."Limit"=e^((5)/(2))`.


Discussion

No Comment Found

Related InterviewSolutions