The velocity of a crawling cell has been modelled as
v ( x ) = 1 a x + e 1 / x {\displaystyle v(x)={\frac {1}{ax+e^{1/x}}}}
where x > 0 {\displaystyle x>0} is the number of actin filaments driving the motion and a > 0 {\displaystyle a>0} is a constant. Determine the following:
(i) lim x → 0 + e 1 / x {\displaystyle \lim _{x\to 0^{+}}e^{1/x}}
(ii) lim x → ∞ e 1 / x {\displaystyle \lim _{x\to \infty }e^{1/x}}
(iii) lim x → 0 + v ( x ) {\displaystyle \lim _{x\to 0^{+}}v(x)}
(iv) lim x → ∞ v ( x ) {\displaystyle \lim _{x\to \infty }v(x)}
is the number of actin filaments driving the motion and 
is a constant. Determine the following:
