Question

If $\underset{x\to 0^{+}}{lim}f\left(x\right)=p$ and $\underset{x\to 0^{-}}{lim}f\left(x\right)=q$, then the wrong statement(s) is\are

• A. $\underset{x\to 0^{-}}{lim}f(x^3-x)=q$
• B. $\underset{x\to 0^{-}}{lim}f(x^3-x)=p$
• C. $\underset{x\to 0^{+}}{lim}f(x^2-x^4)=q$
• D. $\underset{x\to 0^{-}}{lim}f(x^2-x^4)=p$

Answer 1

The correct option is A $\underset{x\to 0^{-}}{lim}f(x^3-x)=q$

$\underset{x\to 0^{+}}{lim}f\left(x\right)=p$ and $\underset{x\to 0^{-}}{lim}f\left(x\right)=q$

When $x\to 0^{-},x^3-x\to 0^{+}⟹\underset{x\to 0^{-}}{lim}f(x^3-x)=p$

When $x\to 0^{-},x^2-x^4\to 0^{-}⟹\underset{x\to 0^{-}}{lim}f(x^2-x^4)=q$

When $x\to 0^{+},x^2-x^4\to 0^{-}⟹\underset{x\to 0^{+}}{lim}f(x^2-x^4)=q$