$5.($Ch $13)(15$ points$)$ Show that the Black$$Scholes$$Merton formula for a call option gives a price that tends to max$($S K$0,0)$ as T$->0.[$Hint: rearrange d$1$ and d$2$ to find the values for N$($d$1)$ and N$($d$2)$ in each scenario, which includes the option is exercised or not exercised. For example, ln$($S K$0/)+($r $+\backslash$sigma $2/2)$T

d$1=$

$=$ T $]$