Question

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = ______.

Options

• 100

• - 100

• 99

• - 99

Answer 1

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = - 99.

Explanation:

`lim_(x -> 1) (1 - (1 - x))^"m"/x` = 99

`=> lim_(x -> 1) ((1 - x)^"n" - 1^"n")/((1 - x) - 1) = - 99`

∴ `"n"/1 (1)^("n - 1") = - 99    ...[because lim_(x -> "a") (x^"m" - "a"^"m")/(x^"n" - "a"^"n") = "m"/"n" "a"^("m - n")]

∴ n = - 99