Science:Math Exam Resources/Courses/MATH102/December 2013/Question B 08/Statement

The velocity of a crawling cell has been modelled as

$v(x)=\frac{1}{ax+e^{1/x}}$

where $x>0$ is the number of actin filaments driving the motion and $a>0$ is a constant. Determine the following:

(i) $\underset{x\to 0^{+}}{\lim }{e}^{1/x}$

(ii) $\underset{x\to \mathrm{\infty }}{\lim }{e}^{1/x}$

(iii) $\underset{x\to 0^{+}}{\lim }v(x)$

(iv) $\underset{x\to \mathrm{\infty }}{\lim }v(x)$