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 equal to

• A. $a^2$
• B. $\frac{1}{a^3}$
• C. $\frac{1}{a^2}$
• D. $a^3$

Answer 1

Answer: (D)

$a^3$

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

(put $x=at$ then $t\to 0$ as $x\to 0$)

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