If _ x k x^3 - k^3 x^2 - k^2 = _ x 0 1 - (2x) x x , then the value of k is

Step-by-step solution

Evaluating the left hand side limit: _ x k x^3 - k^3 x^2 - k^2 = _ x k (x - k)(x^2 + xk + k^2) (x - k)(x + k) = k^2 + k^2 + k^2 k + k = 3k^2 2k = 3k 2 Evaluating the right hand side limit: _ x 0 1 - (2x) x x = _ x 0 2 ^2 x x x = _ x 0 2 ( x x ) = 2(1) = 2 Equating both the limits: 3k 2 = 2 k = 4 3 Answer: 4 3