11. The most general antiderivative of f (a) = (5 - 3x) 4 is OF() = - 21 (5-3x) 4+C OF(x) = - 12 (5 -32) 4 + C I OF(x) = 4 (5 -3x) 4 + C 21 7 OF(x) = (5 -30) 4 +C 1212. An object is red down from a 180m cliff. Four seconds later it strikes a branch sticking out from the cliff which is 40m above the ground. What was the initial velocity of the object. Assume the acceleration due to gravity is -10 m/s2 0 -20 m/s O -15m/s O -30 m/s 0-10 m/s 13. Which of the following would not have the same value as (f (2) - g(2)) dac? O b b If(x)dx - 18(x) dx a a O b - Ig(x) - f(x) ) dx a O I(g(x) - f(x) ) dx b O b I(8(x) - f(x) )dx aThe area between the curve y = $2 and the 3: axis between a: = 0 and a: = 5 is 0 13A units2 ' C] 125 units2 I O 10 units2 0 units2 Math 31 Formula Sheet PreCalculus Applications of Derivatives 43 + BB = (4+ B)42 - AB+ B2 ) $2 - 51 V2 - V1 V avg a avg 43 - B' = (4-B)42 + AB+ B2) 12 - 1 1 12 - 1 1 Triangle: Rectangle: If ax +bx+c=0, then x=-bivb' -4ac =bh A =L . W 2a 2 P = sum of sides P = 2L + 2w m = 2 - V1 y - y1 =m (x-x, ) Circle: Closed Box: (Rect. Prism) X2 - X1 A = m-2 V =L . w. h D= V(x2 -x, ) +(12 - V1) C = 2ar SA = 2L . w+ 2w.h+ 2L .h Sphere: (ball) Closed Cylinder: (can) V = arch Limits SA = 41 1-2 SA = 2xr2 + 2xrh lim f(x) - fla) lim flath)- fla) h-0 Right Angle Cone: x - a h V = arch a(r" -1) if r#1 r-1 SA = 2mrs where s = Vh2+12 S .. a if -1 0 sin x cos x - 1 lim = 0 1- cos x lim [ v(t ) at = s(1) + so Ja(t) at = v(1) + vo