Shadow Position The light from a lamppost casts a shadow from a ball that was dropped from a height of 22 feet above the ground, as shown in the diagram at the top of the right column. The distance d, in feet, the ball has dropped t seconds after it is released is given by Find the distance x, in feet, of the shadow from the base of the lamppost as a function of time t. d = 16t 222 16t 212 ftx feet
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
