Let f(x) = begincases ( ln (8+x3)- ln (8-x3)/x3), textif x ≠ 0 [2ex] k, textif x=0 endcases continuous at x = 0, then the value of k is .

Question

Let f(x) = begincases ( ln (8+x3)- ln (8-x3)/x3), textif x ≠ 0 [2ex] k, textif x=0 endcases continuous at x = 0, then the value of k is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

k= displaystyle limx→ 0 ( ln ((8+x3/8-x3))/x3) = displaystyle limx→ 0 (2 x3/(8-x3) x3) =(1/4)

Q. Let $f (x) = ⎩ ⎨ ⎧ \frac{l n ( 8 + x ^{3} ) - l n ( 8 - x ^{3} )}{x ^{3}}, k, if x \neq = 0 if x = 0$
continuous at $x = 0$ , then the value of k is ______.

$k = x \to 0 lim \frac{ln ( \frac{8 + x ^{3}}{8 - x ^{3}} )}{x ^{3}}$
$= x \to 0 lim \frac{2 x ^{3}}{( 8 - x ^{3} ) x ^{3}}$
$= \frac{1}{4}$

Q. Let f(x)=⎩⎨⎧​x3ln(8+x3)−ln(8−x3)​,k,​if x=0if x=0 ​ continuous at x=0, then the value of k is ______.

k=x→0lim​x3ln(8−x38+x3​)​ =x→0lim​(8−x3)x32x3​ =41​

Q. Let $f (x) = ⎩ ⎨ ⎧ \frac{l n ( 8 + x ^{3} ) - l n ( 8 - x ^{3} )}{x ^{3}}, k, if x \neq = 0 if x = 0$
continuous at $x = 0$ , then the value of k is ______.

$k = x \to 0 lim \frac{ln ( \frac{8 + x ^{3}}{8 - x ^{3}} )}{x ^{3}}$
$= x \to 0 lim \frac{2 x ^{3}}{( 8 - x ^{3} ) x ^{3}}$
$= \frac{1}{4}$