\fMath 31 Formula Sheet PreCalculus Applications of Derivatives 43 + BB = (4+ B)(42 - AB+ B2 ) $2 - $1 V2 - VI V avg t2 - 1 1 a avg 43 - B3 = (4-B)42 + AB + B ) 12 -t1 Triangle: Rectangle: If ax +bx+c=0, then x=- x- - b+vb2 - 4ac = bh A = L . W 2a 2 P = sum of sides P = 2L +2w m = _ Y2 - V1 y -y1 =m ( x-x ) Circle: Closed Box: (Rect. Prism) X2 - X1 A = 1-2 V = L . w. h D = V(x2 -x,)2 + (12 - xi)2 C = 27 SA = 2L . w+ 2w. h+2L . h Sphere: (ball) Closed Cylinder: (can) V = ar h Limits SA = 4xr SA = 2xr2+2arh m, = lim f(x)- fla) = lim flath)- f(a) Right Angle Cone: x- a x - a h -0 h V = arch a(r" -1) if r # 1 r - SA = 2ars where s = Vh2+12 a if -1 0 sin x a COs X - 1 lim 1-cos x lim = 0 X [ ut) at = s(1) + so [a(t) at = v(1)+ vo