Numberline - Calculus - Solved Exam, Exams of Calculus

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Math 105 A and B Exam ITI, page 1. INITIALS March 17, 2006 1. Find all values of A and B for which f(z) = e4" + Bz? is a solution of the differential equation yl + 12y = Ty. / m He onl wy tH eae te? Fist, fal f'fx)= Ae fe avd f"(x) =A%2" for alt xs 8 both Bra =0 fal B20 Now, ‘pg these int the be: : ; 2947 - (4-A-3 bee bawe (hz Ax 08 )+ ae +8x') = Aes 26x) sna A PA a if? 3) (pather "We. ferns" Az Y on 2 Ar?* +120! - Dpe™ + IB +128x°-4Bx =O e(Ar- FA +12) + Bll2x?-Hx +2) = =O a Lo | 2. An object moves along a numberline with position p(t), velocity v(t) and acceleration a(t). Suppose that the acceleration is a(t) = 124? + 16 (ft/sec*), and the velocity at t = 1 is 8 (ft/sec). Suppose also the position at f= 1 is 4 ft 2a. What initial value problem (IVP) is set up to find the formula for v(t) vi(t)= /2t 446 IVP i v(1)= 8 fir wie He ve: viech= WH*st +c hots vives svt) = tere 2b. Solve the IVP in 2a. =f C = B-/6-4 SIL =! Ye Pefod -12 2c. What IVP is set up to find the formula for p(t)? ptt) = Fé 3/et -/2 Iv? 5s | 2d. Solve the [VP in 2c. fet, solve Ae DE: ple) 64+ 8° 12k 4K he’, pli)=4 = pl)= f+ B-i2+K=Y plt)=| £ 4+8e> 2e+? 2e. Where is the object at ¢ = 0? K =49+/2-8-] = 1-9-9 ey uhet 6 plo)? He aves Gnsuer | Z oe