If for p ≠ q ≠ 0 , then function f x = p 729 + x 7 - 3 729 + q x 3 - 9 is continuous at x = 0 , then

Step-by-step solution

For a function to be continuous f x to be x = 0 , we know f 0 = lim x → 0 f x For f x = p 729 + x 7 - 3 729 + q x 3 - 9 limit should be 0 0 from So, lim x → 0 p 729 + x 7 - 3 p . 729 7 - 3 = 0 ⇒ p · 729 = 3 7   ⇒   p = 3 Now, f 0 = lim x → 0 3 3 6 + x 7 - 3 3 6 + q x 3 - 9 = lim x → 0 3 1 + x 3 6 1 7 - 1 9 1 + q x 3 6 1 3 - 1 = 3 9 × 1 7 · 3 6 q 3 · 3 6 ⇒ f 0 = 1 3 × 3 7 q = 1 7 q ⇒ 7 q f 0 - 1 = 0 ⇒ 7 · p 2 · q f 0 -