Question

If $\underset{x\to 0}{lim}\varphi \left(x\right)=a^3,a\ne 0$, then $\underset{x\to 0}{lim}\varphi \left(\frac{x}{a}\right)$ is

• A. $a^2$
• B. $1/a^3$
• C. $1/a^2$
• D. $a^3$

Answer 1

The correct option is D $a^3$

$\underset{x\to 0}{lim}\varphi \left(\frac{x}{a}\right)=\underset{at\to 0}{lim}\left(\frac{at}{a}\right)$
$=\underset{t\to 0}{lim}\varphi \left(t\right)=\underset{x\to 0}{lim}\varphi \left(x\right)=a^3$.