Question

Find \(lt_{p\rightarrow\infty}\frac{p^5.p!}{5.6…(5+p)}\)

(a) 4!

(b) 5!

(c) 0

(d) ∞

This question was posed to me during an internship interview.

This interesting question is from Indeterminate Forms topic in section Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) 4!

To explain I would say: \(=lt_{p\rightarrow\infty}\frac{1.2.3.4}{1.2.3.4}\times \frac{p^5.p!}{5.6…(5+p)}\)

\(=lt_{p\rightarrow\infty}\frac{4!.p^5.p!}{(p+5)!}\)

\(=lt_{p\rightarrow\infty}\frac{4!.p^5}{(p+5)(p+4)(p+3)(p+2)(p+1)}\)

\(=lt_{p\rightarrow\infty}(4!)\times\frac{p^5}{(p+5)(p+4)(p+3)(p+2)(p+1)}=4!\times(1)\)

= 4!