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Question
If `lim_(x->a) (x^9 + "a"^9)/(x + "a") = lim_(x->3)` (x + 6), find the value of a.
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Solution
`lim_(x->a) (x^9 + "a"^9)/(x + "a") = lim_(x->3)` (x + 6)
9 . a9-1 = 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
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