Differentiation Question 495
Question: If $ f(x)=\underset{n,\to ,\infty }{\mathop{\lim }},n({x^{1/n}}-1), $ then for $ x>0,y>0, $ $ f(xy) $ is equal to
Options:
A) $ f(x)f(y) $
B) $ f(x)+f(y) $
C) $ f(x)-f(y) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f(x)=\underset{n\to \infty }{\mathop{\lim }},n({x^{1/n}}-1)=\underset{n\to \infty }{\mathop{\lim }},\frac{{x^{1/n}}-1}{1/n} $ $ =\underset{m\to 0}{\mathop{\lim }},\frac{x^{m}-1}{m}=Inx,( where\frac{1}{n}isreplacedbym ) $ or $ f(xy)=ln(xy)=ln,x+ln,y=f(x)+f(y) $
BETA
