` lim _( x to 0 ) ((1- cos 2 x )(3 + cos x ))/(x tan 4x)` बराबर है :

Options

A. `-(1/4)`
B. `1/2`
C. `1`
D. `2`

Answer

D

Explanation

दिया है : ` lim _( s to 0 ) (( 1- cos 2x)( 3 + cos x))/( x tan 4x)`
` = lim _( x to 0 ) ( 2 sin ^(2) x )/x xx (( 3+ cos x)x)/(x tan 4x ) `
` = lim _( x to 0 ) ( sin^(2) x)/(x^(2)) xx ( 3 + cos x) /1 xx x/( tan 4x)`
` = 2 lim _( x to 0 ) ( sin^(2) x )/(x^(2)) xx (3+ cos x)/1 xx x /( tan 4x)`
` = 2 lim _( x to 0 ) (( sinx)/x)^(2) xx lim _( x to 0 ) ( 3 + cos x ) xx 1/4 lim _( 4 to 0 ) (4x)/( tan 4x)`
` = 2 xx 1 xx ( 3+ 1 ) xx1/4`
` = 2 xx 4 xx 1/4 = 2 `