Additional Problem A

$($a$)$ Find $\underset{x}{lim}\frac{\sqrt[\phantom{2}]{x}}{\sqrt[\phantom{2}]{x1}}.$

$($b$)$ Find $\underset{x}{lim}\frac{\sqrt[\phantom{2}]{x\sqrt[\phantom{2}]{x}}}{\sqrt[\phantom{2}]{x1}}.$

$($c$)$ Find $\underset{x}{lim}\frac{\sqrt[\phantom{2}]{x\sqrt[\phantom{2}]{x\sqrt[\phantom{2}]{x}}}}{\sqrt[\phantom{2}]{x1}}.$

Additional Problem B

Find $\underset{x}{lim}x-\sqrt[3]{x^3-1}.$

Hint: we remind you that $a^3-b^3=(a-b)(a^{2}ab{b}^2).$