1. Differentiation A Slippery Slope - Jerks You Around - Accelerates Your Mind http://nm.mathforcollege.com

2. Oil Spill Time (s )00.51.01.52.02.53.03.54.04.55.0 Radius(m )00.2360.6671.2251.8862.6353.4644.3655.3336.3647.454 http://nm.mathforcollege.com

3. Acceleration of a rocket http://nm.mathforcollege.com

4. 2.01 BACKGROUND http://nm.mathforcollege.com

5. To find location from velocity vs time data of the body, the mathematical procedure used is A.Differentiation B.Integration http://nm.mathforcollege.com

6. The definition of the exact derivative of the function f (x) is A. B. C. D. http://nm.mathforcollege.com

7. The exact derivative of f (x)=x 3 at x=5 is most nearly A.25.00 B.75.00 C.106.25 D.125.00 http://nm.mathforcollege.com

8. Given y=5e 3x + sinx, dy/dx is 1. 5e 3x + cos(x) 2. 15e 3x + cos(x) 3. 15e 3x – cos(x) 4. 2.666e 3x – cos(x) http://nm.mathforcollege.com

9. Given y=sin(2x), dy/dx at x=3 A.0.9600 B.0.9945 C.1.920 D.1.989 http://nm.mathforcollege.com

10. END http://nm.mathforcollege.com

11. 02.02 CONTINUOUS FUNCTIONS http://nm.mathforcollege.com

12. Given f (x)=x 2, using forwarded divided difference scheme and step size of 0.2, the value of f ′ (6) most nearly is A.11.8 B.12.0 C.12.2 D.36.0 http://nm.mathforcollege.com

13. Using forwarded divided difference with a step size of 0.2, the derivative of f(x)=5e 2.3x at x=1.25 is A. 258.8 B. 163.4 C. 211.1 D. 203.8 http://nm.mathforcollege.com

14. The order of accuracy of the forwarded divided difference approximation 1)O(h) 2)O(h 2 ) 3)O(h 3 ) http://nm.mathforcollege.com is

15. The highest order of polynomial for which the forward divided difference gives the exact answer for its first derivative at any point is A. 0 B. 1 C. 2 D. 3 10 http://nm.mathforcollege.com

16. Using forward divided difference, the true error in the calculation of a derivative of a function is 32.0 for a step size of 0.4. If the step size is reduced to 0.1, the true error will be approximately A. 2.0 B. 4.0 C. 8.0 D. 16.0 10 http://nm.mathforcollege.com

17. The highest order of polynomial for which the central divided difference gives the exact answer for its first derivative at any point is A. 0 B. 1 C. 2 D. 3 10 http://nm.mathforcollege.com

18. The order of accuracy of the central divided difference approximation 1)O(h) 2)O(h 2 ) 3)O(h 3 ) http://nm.mathforcollege.com is

19. Using central divided difference, the true error in the calculation of a derivative of a function is 32.0 for a step size of 0.4. If the step size is reduced to 0.1, the true error will be approximately A. 2.0 B. 4.0 C. 8.0 D. 16.0 10 http://nm.mathforcollege.com

20. A function is differentiable and all its derivatives are also differentiable between 0 and 10. Given f (2 )=7, f ′(2)=12 and all other derivatives of f(x) at x=2 are zero, the value of f (5) is 1. 36 2. 43 3. 60 4. Cannot be found http://nm.mathforcollege.com

21. END http://nm.mathforcollege.com

22. 02.03 DISCRETE FUNCTIONS http://nm.mathforcollege.com

23. The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s 2 is t (s)00.51.11.51.8 v (m/s)0213223275300 A.83.33 B.128.33 C.173.33 D.183.33 http://nm.mathforcollege.com

24. The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s 2 is t (s)00.51.21.51.8 v (m/s)0213223275300 A.83.33 B.128.33 C.173.33 D.183.33 http://nm.mathforcollege.com

25. Allowed to use only a second order polynomial to approximate velocity, the data points you would choose to find the velocity of the rocket at t=1.1s are t (s)00.51.21.51.8 v (m/s)0213223275300 A.t=0, 0.5, 1.2 B.t=0.5, 1.2, 1.3 C.t=1.2, 1.3, 1.4 D.t=0, 1.2, 1.4 http://nm.mathforcollege.com

26. The velocity vs time is given below. The values at t=1.2, 1.5 and 1.8 are interpolated to a 2 nd order polynomial. t(s)00.51.21.51.8 v(m/s)0213223275300 The best estimate of acceleration at t=1.5 in m/s 2 is A. 83.33 B. 128.33 C. 173.33 D. 275.00 http://nm.mathforcollege.com

27. In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E(t), Time, t (secs)1.001.011.031.1 Current, i (amperes)3.103.123.183.24 If L=0.98 henries and R=0.142 ohms, find E(1.00) with most accuracy and choosing amongst FDD, BDD or CDD. A. B. C. D. http://nm.mathforcollege.com

28. END http://nm.mathforcollege.com