If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k =

Step-by-step solution

For the function to be continuous at x = 0 , we must have _ x 0 f(x) = f(0) = k . _ x 0 1+x - 1-x x Rationalizing the numerator: = _ x 0 ( 1+x - 1-x )( 1+x + 1-x ) x ( 1+x + 1-x ) = _ x 0 (1+x) - (1-x) x ( 1+x + 1-x ) = _ x 0 2x x ( 1+x + 1-x ) Using the standard limit _ x 0 x x = 1 : = _ x 0 2 1+x + 1-x _ x 0 x x = 2 1+0 + 1-0 1 = 2 2 = 1 Therefore, k = 1 . Answer: 1