Question

[(x³⁶⁵ – 365x + 364)/(x – 1)²] for lim x→1 = ?

(a) 66,430 

(b) 64,340 

(c) 66,630 

(d) 64,430

Answer 1

The correct option (a) 66,430

Explanation:

lim_x→1 [(x³⁶⁵ – 365x + 364)/(x – 1)²]

= lim_x→1 [(x³⁶⁵ – 1 – 365x + 365)/(x – 1)²]

= lim_x→1 [{(x – 1)(x³⁶⁴ + x³⁶³ + .... 1) – 365(x – 1)}/(x – 1)²]
= lim_x→1 [{(x³⁶⁴ + x³⁶³ + .... 1) – (1 + 1 + 1+ .... 365 times)}/(x – 1)]

= lim_x→1 [{(364x³⁶³ + 363x³⁶² + 362x³⁶¹ + ..... 0) – 0}/(1 – 0)]

(∵ lim_x→a [{f(x)}/{g(x)}] = lim_x→a [{f'(x)}/{g'(x)}])

= [(364 + 363 + 362 + ..... 0)/1]

= sum of A.P.

= (365/2) (364 + 0)

= 66,430.