Advertisements
Advertisements
Question
Find ‘n’ if `lim_(x -> 2) (x^n - 2^n)/(x - 2)` = 80, x ∈ N
Sum
Solution
Given that `lim_(x -> 2) (x^n - 2^n)/(x - 2)` = 80
= `n * (2)^(n - 1)` = 80 .....`[because lim_(x -> a) (x^n - a^n)/(x - a) = n * a^(n - 1)]`
= `n xx 2^(n - 1)`
= `5 xx (2)^(5 - 1)`
∴ n = 5
shaalaa.com
Derive Derivation of x^n
Is there an error in this question or solution?
