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If [.] denotes the greatest intger funct...

If `[.]` denotes the greatest intger function, then `lim_(xrarr0) (tan([-2pi^2]x^2)-x^2tan[-2pi^2])/(sin^2x)` is equal to

A

`20 +tan 20`

B

`-20+tan 20`

C

`20`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `[-2pi^2]=-20`.
`therefore lim_(xto0) (tan([-2pi^2]x^2)-x^2tan[-2pi^2])/(sin^2x)`
`=lim_(xto0) (tan(-20x^2)-x^2tan(-20))/(sin^2x)`
`=lim_(xto0) -(tan20x^2)/(20x^2)xx20xx(x^2)/(sin^2x)xx((x)/(sinx))^2tan20 =-20+tan20`.
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