Maharashtra State BoardHSC Commerce 11th
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If limx→2xn-2x-2 = 80 then find the value of n. - Mathematics and Statistics

Sum

if `lim_(x -> 2) (x^"n"- 2^"n")/(x - 2)` = 80 then find the value of n.

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Solution

`lim_(x -> 2) (x^"n"- 2^"n")/(x - 2)` = 80

∴ n(2)n–1 = 80       ...`[lim_(x -> "a") (x^"n" - "a"^"n")/(x - "a") = "na"^("n" - 1)]`

∴ n(2)n–1 = 5 x 16
= 5 x (2)4
∴ n(2)n –1 = 5 x (2)5–1
∴ n = 5

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 7 Limits
Miscellaneous Exercise 7 | Q I. (1) | Page 105
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