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underset(xrarr0)(lim)(1)/(x^(2))|(1-cos3...

`underset(xrarr0)(lim)(1)/(x^(2))|(1-cos3x,log_(e)(1+4x)),(sin^(-1)(e^(x)-1),tan^(-1)(2x))|`

A

2

B

`-4`

C

6

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xrarr0)(lim)(1)/(x^(2))|(1-cos3x,log_(e)(1+4x)),(sin^(-1)(e^(x)-1),tan^(-1)(2x))|`
`=underset(xrarr0)(lim)|((1-cos3x)/(x),(log_(e)(1+4x))/(x)),((sin^(-1)(e^(x)-1))/(x),(tan^(-1)(2x))/(x))|`
`=|(underset(xrarr0)(lim)(1-cos3x)/(x),underset(xrarr0)(lim)(log_(e)(1+4x))/(x)),(underset(xrarr0)(lim)(sin^(-1)(e^(x)-1))/(x),underset(xrarr0)(lim)(tan^(-1)(2x))/(x))|`
`=|(0,4),(1,2)|=-4`
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