1. Solve the differential equation 3;! = y3, y(3) = %. 0 None of the other answers is correct 2. Consider the differential equation % = y sin(:r:) with initial condition (7r, 3). First solve this to find 31(3), and then use your answer to nd y( g). on 3_If fl (:3) : 49:00:1(932) and 3' () = 9, ndf (g). 06 4. Solve the equation = -r + cos(x) for y, if y(7) = 6. O y= -12 + sin(x) + 12 +7 O y= - 2 + sin(x) + +6 O 5+ cos() O y= 7+cos(37) O y= - 4 + cos(x) - +5 5. The rate at which a certain bacteria population grows is modeled by the equation ~ = ky. Ify = 123 when t = 1 and y = 357 when t =3, what is the rate of growth of the bacteria population? O 357 1B( 7-) 119 41 O 119 41 123 V 110 O In( 128 O In() 26. The slope field for a specific differential equation is shown below. w N - O -2 w -4 -4 -3 -2 -1 0 1 2 3 Which of the following could be a solution to the differential equation with an initial condition of y(0) = 2? O y=2-x2 O y=2-2x O y=x2+2 O y = 2 -2 O y=2( + 2)7. The slope field for a specific differential equation is shown below. w N WN JO - -3 0 Which of the following could be a solution to the differential equation with an initial condition of y(1) = -2? O y= 4 la(2) - 2 O y = la(2) + 2 O y= 2 O y= Va - 1-2 O y=4vx +18. Which differential equation describes the slope field shown below? w N - w Ny O A O -3 -2 2 O dy = (202 - 1) O du = (x2+1)+y dy =y-1+ dy =0-1 ag = x+19. Which of the following slope fields describes the differential equation w 2 O 4 N -4 N -3 -2 w N - O N w -4 -3 -2 -1 0 1 2 3 W N N LO - - 4 -3 -2 0 3 W 2\f10. What is the formula for the line tangent to the curve f (z) 2 003(3) at x = 7r? 11. What is the formula of the line tangent to the curve 1' (m) = Z at a: : 4? O y=(m4) 12. What formula would be used to calculate a local linear appromation for f (m) = 33'\" around a: = 1? O y=333(m~1) O y=3e3m~233 O y=3eam+e3 O y=3 0 Few 13. Find the integral of 14 3+ 14+ 14 O 2 7:2 - 71x| + C 2 - 7x + 7lax|+C O 7:4 + 7x + 7lax| +C O 7:' + 7x + 71 x| +C O 2+7x+ C 14. f( cost x sin x) da = O sin' + C O GOB & + C sin & cos & + C 5 sin a cos & + C 5 C CO8 & + C 6 43+8x2 4x is 15. limz-+00 8346%248 O 2/3 1/24 1/8 1/3 3/816. Solve for y(t) if the following adheres to the exponential growth/ decay,r model. y(0)=32 and the rate of growth is 2.8% 316) = Keanzsssz y(t) = 0.028332 y(t) = [3.028332t y(t) = 32383239\" y\") = 328013283 17. The rate of growth of a lizard population in a small area of the Mojave desert is proportional to the amount of lizards already in the population. If the population grows continually at a rate of 11%, and there are originally 250 lizards in the population, how many months does it take for the lizard population to triple? O 2.938 months 0 5.638 months 0 1.104 months 0 9.987 months 0 10.532 months 18. A cup of hot chocolate is sitting on the counter, but it is too hot to drink. The room is a constant temperature of 7201'?I and the temperature hot chocolate is originally measured to be 1939131 After 2 minutes, the temperature is measured again, and the hot chocolate is 1790F. After how many total minutes must you wait before the hot chocolate reaches the optimal drinking temperature of 150013? HINT: Newton's Law of Cooling is T = (To Takel\" + Ta 0 it = 4.19 minutes 0 it = 5.49 minutes 0 t = 7.14 minutes 0 t = 4.80 minutes 0 t = 2.19 minutes . . - d? _ 19. A population P grows according to the equatlon E kP. If the population of P doubles every 41 years, What is the value of k? 0 k = 0.030 O k = 0.021 O k = 0.024 O k = 0.017 O k = 0.028 20. (% error) = (actual value)-(approximated value)| (actual value X 100% Use the formula above to find the answer to the following question: If the local linear approximation of f (x) = @ at x-2 is used to find the approximation for f (2.2), then the % error of this approximation is... O less than 2%. O between 2% and 5%. O between 5% and 8%. O between 8% and 11%. O between 11% and 14%. 21. 59 12 sin( da Using the substitution 0 = -Vx, which of the following is equivalent to the above integral? Let Va > 0. O -24fi sin(0) de O -12fi sin(0) de O - 6fi sin(0) de O -24 sin(0) de O -12[ sin(0) de