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lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-t...

`lim_(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1))` is equal to (a) 1 (b) 0 (c) 2 (d) none of these

A

-1

B

1

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1))`
`(x^(4)(1-tan^(2)x+tan^(4)x))/(tan^(4)x(tan^(4)x-tan^(2)x+1))=(x^(4))/(tan^(4)x),xne0`
`:." "underset(xto0)lim(x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1))=underset(xto0)lim(x^(4))/(tan^(4x))=1`
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