Navigation As we have seen in previous chapters, the great circle distance (in radians) between two points PI(LTI , LN1) and P2(LT2, LN2), whose coordinates are given as latitudes and longitudes, is calculated using the formula d COS-I (sin (LTI) sin (LT2) + cos (LT1) cos (LT2) cos (LNI - LN2 An alternate formula that can be used is ( .. LT} LT2 LN! LN2 d 1.;n-' Y,;n'( 2 ) + co, (LT,) 00' (LT,) sill' ( 2 )) Prove that by setting these two expressions equal to one another, the result is an identity.

Calculus 3 Week 3: Limits Recall in 1 dimension, if we have that the x→a f (x)=L if when we approach a from both sides and the limit is L, then the limit exists and is L. There’s not much else to explain so let’s get right to it. Examples Determine if the following limits exist and if so, find the limit lim xycos zπ )+5 a) (x,y,=(2,3,6) Just plug in the values since the function is defined everywhere. 6cos (6π +5=11 So the limit exists and is 11. lim 3x+y b) (x =(2,3)1 x−y 2 1 The limit will not exist ay y= x . But this is no problem on the bottom since we don’t