Let l= underset x arrow 0+ textLim x m ( ln x ) n where m , n ∈ N then :

Question

Let l= underset x arrow 0+ textLim x m ( ln x ) n where m , n ∈ N then : (A) l is independent of m and n (B) l is independent of m and depends on m (C) l is independent of n and dependent on m (D) l is dependent on both m and n

Tardigrade Admin · Accepted Answer

l= underset x arrow 0+ textLim (( ln x ) n / x - m ) Using L'Hospital's rule l underset x arrow 0+ textLim ( n !(-1) n / m n ) x m =0

Q. Let $l = x \to 0^{+} Lim x^{m} (ln x)^{n}$ where $m, n \in N$ then :

l is independent of m and n

l is independent of m and depends on m

l is independent of n and dependent on m

l is dependent on both m and n

$l = x \to 0^{+} Lim \frac{( l n x ) ^{n}}{x ^{- m}}$
Using L'Hospital's rule $l x \to 0^{+} Lim \frac{n ! ( - 1 ) ^{n}}{m ^{n}} x^{m} = 0$

Q. Let l=x→0+Lim​xm(lnx)n where m,n∈N then :