Question

Limit Xtends to 0
(1+sinx)^⅓-(1-sinx)^⅓/x ​

Answer 1

Answer:

Step-by-step explanation:

Limit Xtends to 0  ((1+sinx)^⅓-(1-sinx)^⅓)/x = 0/0

use L'Hôpital's rule

Limit Xtends to 0  ((1+sinx)^⅓-(1-sinx)^⅓)/x

=​ Limit Xtends to 0   ( d(1+sinx)^(1/3))/dx - d(1-sinx)^(1/3))/dx ) / (dx/dx

= Limit Xtends to 0  ( (1/3)(1+sinx)^(-2/3)cosx-(1/3)(1-sinx)^(-2/3)(-cosx) )

= (1/3)(1+0)^(-2/3)(1)-(1/3)(1-0)^(-2/3)(-1)

= (1/3)+(1/3)

=2/3