`lim_(xrarr0) (1)/(x^(2))|(1-cos3x,log_(e)(1+4x)),(sin^(-1)(x^(x)-),tan^(-1)(2x))|` is equal to

Options

A. 2
B. `-4`
C. 6
D. 4

Answer

B

Explanation

`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`