1. Differentiation A Slippery Slope - Jerks You Around - Accelerates Your Mind

2. http://numericalmethods.eng.usf.e du Identify the picture of your instructor A. B. C. D.

3. 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

4. Acceleration of a rocket

5. BACKGROUND

6. To find location from velocity vs time data of the body, the mathematical procedure used is A.Differentiation B.Integration

7. The definition of the exact derivative of the function f (x) is A.. B.. C.. D..

8. Given y=sin(2x), dy/dx at x=3 A.0.9600 B.0.9945 C.1.920 D.1.989

9. END

10. CONTINUOUS FUNCTIONS

11. 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

12. The order of accuracy of the forwarded divided difference approximation as given by formula below is 1)O(h) 2)O(h 2 ) 3)O(h 3 )

13. The order of accuracy of the central divided difference approximation as given by formula below is 1)O(h) 2)O(h 2 ) 3)O(h 3 )

14. 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

15. 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

16. 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

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

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19. DISCRETE FUNCTIONS

20. This is what you have been saying about your TI-30Xa http://numericalmethods.eng.usf.e du A.I don't care what people say The rush is worth the price I pay I get so high when you're with me But crash and crave you when you are away B.Give me back now my TI89 Before I start to drink and whine TI30Xa calculators make me cry Incarnation of of Jason will you ever die C.TI30Xa – you make me forget the high maintenance TI89. D.I never thought I will fall in love again!

21. The velocity vs. time is given below. The best estimate of acceleration at t=1.5 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

22. 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

23. END

24. Extra Questions you can do at home

25. 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

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 1. 83.33 2. 128.33 3. 173.33 4. 275.00

27. 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)

28. Using forward 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

29. Using forward divided difference with a step size of 0.2, the derivative of the function at x=2 is given as x1.82.02.22.42.6 f(x)6.04967.38909.025011.02313.464 1.6.697 2.7.389 3.7.438 4.8.179

30. 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, how would you find E(1.00), what would be your choice for most accuracy. 1. 2. 3. 4.

31. 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

33. 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