If limx→2xn-2nx-2=448, then find the least positive integer n.

If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.

Sum

`lim_(x->2) (x^n - 2^n)/(x-2) = 448`

i.e., n 2^n-1 = 7 × 2⁶

n × 2^n-1 = 7 × 2^7-1

∴ n = 7

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Limits and Derivatives

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Chapter 5: Differential Calculus - Exercise 5.2 [Page 110]

Chapter 5 Differential Calculus
Exercise 5.2 | Q 3 | Page 110

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