displaystyle limx → 1 (xm-1/xn-1) is

Question

displaystyle limx → 1 (xm-1/xn-1) is (A) 1 (B) (m/n) (C) -(m/n) (D) (m2/n2)

Tardigrade Admin · Accepted Answer

We have, displaystyle limx → 1 (xm-1/xn-1) = displaystyle limx → 1 (xm-1m/x-1)× (x-1/xn-1n) = displaystyle limx → 1 (xm-1m/x-1) × displaystyle limx → 1 (x-1/xn-1n) =(m(1)m-1/n(1)n-1)=(m/n)

Q. $x \to 1 lim$ $\frac{x ^{m} - 1}{x ^{n} - 1}$ is

$1$

$\frac{m}{n}$

$- \frac{m}{n}$

$\frac{m ^{2}}{n ^{2}}$

Q. x→1lim​ xn−1xm−1​ is

1

nm​

−nm​

n2m2​

We have, x→1lim​ xn−1xm−1​ =x→1lim​ {x−1xm−1m​×xn−1nx−1​} =x→1lim​{x−1xm−1m​}×x→1lim​ {xn−1nx−1​} =n(1)n−1m(1)m−1​=nm​

Q. $x \to 1 lim$ $\frac{x ^{m} - 1}{x ^{n} - 1}$ is

$1$

$\frac{m}{n}$

$- \frac{m}{n}$

$\frac{m ^{2}}{n ^{2}}$