displaystyle lim x arrow 0 (x √[3]z2-(z-x)2/(√[3]8 x z-4 x2+√[3]8 x z)4) is equal to

Question

displaystyle lim x arrow 0 (x √[3]z2-(z-x)2/(√[3]8 x z-4 x2+√[3]8 x z)4) is equal to (A) ( z /211 / 3) (B) (1/223 / 3 ⋅ z ) (C) 221 / 3 z (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 0 (x √[3]z2-(z-x)2/(√[3]8 x z-4 x2+√[3]8 x z)4) = displaystyle lim x arrow 0 (x √[3]2 x z-x2/(√[3]x √[3]8 z-4 x+√[3]8 z √[3]x)4) = displaystyle lim x arrow 0 (x4 / 3 √[3]2 z-x/x4 / 3[√[3]8 z-4 x+√[3]8 z]4) =(√[3]2 z/[2 √[3]8 z]4)=(1/223 / 3 ⋅ z)

Q. $x \to 0 lim \frac{x 3 z ^{2} - ( z - x ) ^{2}}{( 3 8 x z - 4 x ^{2} + 3 8 x z ) ^{4}}$ is equal to

$\frac{z}{2 ^{11/3}}$

$\frac{1}{2 ^{23/3} \cdot z}$

$2^{21/3} z$

None of these

Q. x→0lim​(38xz−4x2​+38xz​)4x3z2−(z−x)2​​ is equal to

211/3z​

223/3⋅z1​

221/3z

None of these

x→0lim​(38xz−4x2​+38xz​)4x3z2−(z−x)2​​ =x→0lim​(3x​38z−4x​+38z​3x​)4x32xz−x2​​ =x→0lim​x4/3[38z−4x​+38z​]4x4/332z−x​​ =[238z​]432z​​=223/3⋅z1​

Q. $x \to 0 lim \frac{x 3 z ^{2} - ( z - x ) ^{2}}{( 3 8 x z - 4 x ^{2} + 3 8 x z ) ^{4}}$ is equal to

$\frac{z}{2 ^{11/3}}$

$\frac{1}{2 ^{23/3} \cdot z}$

$2^{21/3} z$