Question

If $na^{n}$ , then

• A. $\lim_{h \rightarrow 0}\frac{1}{h}\left\lbrack \frac{1}{x + h} - \frac{1}{x} \right\rbrack$
• B. $\frac{1}{2x}$
• C. $- \frac{1}{2x}$ is discontinuous at $\frac{1}{x^{2}}$
• D. None of these

Answer 1

Answer: (C)

$- \frac{1}{2x}$ is discontinuous at $\frac{1}{x^{2}}$

Answer 2

$f ( 1 - ) = \lim _ { x \rightarrow 1 - } \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 1 } = - 1 \Rightarrow f ( 1 ) \neq f ( 1 - )$

Hence the function is discontinuous at $x = 1$ .