Question

If `lim_(x->a) (x^9 + "a"^9)/(x + "a") = lim_(x->3)` (x + 6), find the value of a.

Answer 1

`lim_(x->a) (x^9 + "a"^9)/(x + "a") = lim_(x->3)` (x + 6)

9 . a^9-1 = 3 + 6

9 . a⁸ = 9

a⁸ = 1

Taking squareroot on bothsides, we get

`("a"^8)^(1/2) = +-1`

a⁴ = ±1

But a⁴ = -1 is imposssible.

∴ a⁴ = 1

Again taking squareroot, we get

`("a"^4)^(1/2) = +-1`

a² = ±1

a² = -1 is imposssible

∴ a² = 1

Again taking positive squareroot, a = ±1