Question

$\underset{x\to a}{lim}\frac{1}{(x-a{)}^{2n-1}}\left(nϵN\right)$ equals

• A. $\infty$
• B. $-\infty$
• C. $0$
• D. does not exist

Answer 1

The correct option is D does not exist

Left hand limit is $=\underset{x\to a^{-}}{lim}\frac{1}{(x-a{)}^{2n-1}}=-\infty$

And Right hand limit is $=\underset{x\to a^{+}}{lim}\frac{1}{(x-a{)}^{2n-1}}=+\infty$

$L.H.L.\ne R.H.L.$

Therefore, the given limit does not exist.
Hence, the option 'D' is correct.