The value of undersetx arrow 0l i m(l n (10 - 9 cos 2 x)/l n2 (sin â¡ 3 x + 1)) is equal to

Question

The value of undersetx arrow 0l i m(l n (10 - 9 cos 2 x)/l n2 (sin â¡ 3 x + 1)) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

undersetx arrow 0l i m(l n (10 - 9 cos 2 x)/l n2 (sin â¡ 3 x + 1))= undersetx arrow 0l i m(l n 1 + (9 - 9 cos â¡ 2 x) /l n2 (1 + sin â¡ 3 x)) = undersetx arrow 0l i m(9 (1 - cos 2 x)/(sin â¡ 3 x)2)= undersetx arrow 0l i m(9 (2 x2)/(3 x)2)=2

Q. The value of $x \to 0 l im \frac{l n ( 10 - 9 cos 2 x )}{l n ^{2} ( s in 3 x + 1 )}$ is equal to

$x \to 0 l im \frac{l n ( 10 - 9 cos 2 x )}{l n ^{2} ( s in 3 x + 1 )} = x \to 0 l im \frac{l n { 1 + ( 9 - 9 cos 2 x ) }}{l n ^{2} ( 1 + s in 3 x )}$
$= x \to 0 l im \frac{9 ( 1 - cos 2 x )}{( s in 3 x ) ^{2}} = x \to 0 l im \frac{9 ( 2 x ^{2} )}{( 3 x ) ^{2}} = 2$

Q. The value of x→0lim​ln2(sin⁡3x+1)ln(10−9cos2x)​ is equal to

x→0lim​ln2(sin⁡3x+1)ln(10−9cos2x)​=x→0lim​ln2(1+sin⁡3x)ln{1+(9−9cos⁡2x)}​ =x→0lim​(sin⁡3x)29(1−cos2x)​=x→0lim​(3x)29(2x2)​=2

Q. The value of $x \to 0 l im \frac{l n ( 10 - 9 cos 2 x )}{l n ^{2} ( s in 3 x + 1 )}$ is equal to

$x \to 0 l im \frac{l n ( 10 - 9 cos 2 x )}{l n ^{2} ( s in 3 x + 1 )} = x \to 0 l im \frac{l n { 1 + ( 9 - 9 cos 2 x ) }}{l n ^{2} ( 1 + s in 3 x )}$
$= x \to 0 l im \frac{9 ( 1 - cos 2 x )}{( s in 3 x ) ^{2}} = x \to 0 l im \frac{9 ( 2 x ^{2} )}{( 3 x ) ^{2}} = 2$