a. What is the area enclosed by the curves y = x∧3 – 8x∧2 + 18x -5 and y = x + 5? a. 10.667 b. 11.833 c. 14.583 d. 21.333 e. 32 b. An object traveling in a straight line has position x(t) at time t. If the initial position is x(0) = 2 and the velocity of the object is v(t) = (1 + t∧2)∧(1/3), what is the position of the object at time t = 3? a. 0.431 b. 2.154 c. 4.512 d. 6.512 e. 17.408 c. On the graph of y = f(x), the slope at any point (x,y) is twice the value of x. If f(2)= 3, what is the value of f(3) a. 6 b. 7 c. 8 d. 9 e. 10

## Answer

a for intersection 23-8x?+18x – 5 = 2+5 z?-822+19% -10=0 1, 2,5 areu will be as 2 A = -3x+181-5). 1 (zdas ) À = $ 22-83°4182-5 ) – 6645) Jdz+ 5*[(x+3) – 67%82*+82-5)] de 1 (? + s (-x?482?–174 +10) de As con – %) ( **+ BR-174 2 Hom), 2 A= s 1 2 2 + 5 A = 7 12 + 45 4 A = 11.333 ophon thal 1 we know Va da dt vdt by integrating both sides 3 dt ?’* ļo++)” } 1’itez” dat X 13) – X(0)= 6 X (3)=-25 4-512 X(3) = 6.512 optim ☺

a ya flug slobe f (x) given F'(x) = 2x by integrating Sf'(x1 = (2x dx Fix) = n2+ c ginen f(2)= 3 3= 4 to -> (5-1 2 f(x)= x2-1 f(3) = (3) 21 f(3) = 9-1 f(3) = optim ©