Recall that the area of an ellipse with radii a and b is giv

Recall that the area of an ellipse with radii a and b is given by A = a b. Consider an ellipse with radii a = 51.2 and b = 25.9.

(a) Find the exact of the ellipse using your calculator.

(b) Estimate the area of the ellipse using differentials. Give your to 3 places past the decimal.

area A = a b ,a=51.2 , b=25.9

(a)

exact area = *51.2*25.9

exact area = 1326.08

exact area 4166.003

(b)

A = a b

dA = ((da *b) +(a* db))

a=50, b=25, da=1.2 ,db=0.9

area of the ellipse using differentials =( a b)+(((da *b) +(a* db)))

area of the ellipse using differentials =(*50*25)+(((1.2 *25) +(50* 0.9)))

area of the ellipse using differentials =(1250)+(75)

area of the ellipse using differentials =1325

area of the ellipse using differentials =4162.610