displaystyle lim h arrow 0((1/h √[3]8+h)-(1/2 h)) equals to

Question

displaystyle lim h arrow 0((1/h √[3]8+h)-(1/2 h)) equals to (A) -(1/8) (B) (1/8) (C) (1/48) (D) -(1/48)

Tardigrade Admin · Accepted Answer

displaystyle lim h arrow 0 (2-√[3]8+h/2 h ⋅ √[3]8+h) = displaystyle lim h arrow 0 (8-(8+h)/2 h ⋅ √[3]8+h 82 / 3+81 / 3 ⋅(8+h)1 / 3+(8+h)2 / 3 ) =-(1/48)

Q. $h \to 0 lim (\frac{1}{h 3 8 + h} - \frac{1}{2 h})$ equals to

$- \frac{1}{8}$

$\frac{1}{8}$

$\frac{1}{48}$

$- \frac{1}{48}$

$h \to 0 lim \frac{2 - 3 8 + h}{2 h \cdot 3 8 + h}$
$= h \to 0 lim \frac{8 - ( 8 + h )}{2 h \cdot 3 8 + h { 8 ^{2/3} + 8 ^{1/3} \cdot ( 8 + h ) ^{1/3} + ( 8 + h ) ^{2/3} }}$
$= - \frac{1}{48}$

Q. h→0lim​(h38+h​1​−2h1​) equals to

−81​

81​

481​

−481​