Question

Find: $\underset{x\to 0^{+}}{lim}\frac{1}{x}$

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

Answer 1

The correct option is C $\infty$

$\underset{x\to 0^{+}}{lim}\frac{1}{x}=\underset{y\to 0}{lim}\frac{1}{0+h}=+\infty$

we have to define $\delta$ $st0<x<\delta$

$then\frac{1}{x}>M\Rightarrow x<\frac{1}{M}$

$choose\delta =\frac{1}{M}\to 0<x<\delta \to \frac{1}{x}>M$

$\underset{x\to 0}{lim}+\frac{1}{x}=+\infty$