The value of displaystyle limx → 3 (x5-35/x8-38) is equal to

Question

The value of displaystyle limx → 3 (x5-35/x8-38) is equal to (A) (5/8) (B) (5/64) (C) (5/216) (D) (1/27)

Tardigrade Admin · Accepted Answer

lim limits x arrow 3 (x5-35/x8-38) (. form .(0/0)) = lim limits x arrow 3 (5 x4/8 x7) (L'Hospital's rule) = lim limitsx arrow 3 (5/8 x3)=(5/8 × 33)=(5/8 × 27)=(5/216)

Q. The value of $x \to 3 lim \frac{x ^{5} - 3 ^{5}}{x ^{8} - 3 ^{8}}$ is equal to

$\frac{5}{8}$

$\frac{5}{64}$

$\frac{5}{216}$

$\frac{1}{27}$

$\frac{1}{63}$

$x \to 3 lim \frac{x ^{5} - 3 ^{5}}{x ^{8} - 3 ^{8}} ($ form $\frac{0}{0})$
$= x \to 3 lim \frac{5 x ^{4}}{8 x ^{7}}$ (L'Hospital's rule)
$= x \to 3 lim \frac{5}{8 x ^{3}} = \frac{5}{8 \times 3 ^{3}} = \frac{5}{8 \times 27} = \frac{5}{216}$

Q. The value of x→3lim​x8−38x5−35​ is equal to

85​

645​

2165​

271​

631​

x→3lim​x8−38x5−35​( form 00​) =x→3lim​8x75x4​ (L'Hospital's rule) =x→3lim​8x35​=8×335​=8×275​=2165​