Differentiation Question 188
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)=lnx+lny=f(x)+f(y) $
BETA
