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

1. DifferentiationA Slippery Slope - Jerks You Around - Accelerates Your Mind

2. Identify the picture of your instructor http://numericalmethods.eng.usf.edu

3. Oil Spill

4. Acceleration of a rocket

5. BACKGROUND

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

7. The definition of the exact derivative of the function f (x) is • . • . • . • . 10

8. Given y=sin(2x), dy/dx at x=3 • 0.9600 • 0.9945 • 1.920 • 1.989 10

9. END

10. CONTINUOUS FUNCTIONS

11. Given f (x)=x2, using forwarded divided difference scheme and step size of 0.2, the value of f ′ (6)most nearly is • 11.8 • 12.0 • 12.2 • 36.0 10

12. The order of accuracy of the forwarded divided difference approximation as given by formula below is • O(h) • O(h2) • O(h3)

13. The order of accuracy of the central divided difference approximation as given by formula below is • O(h) • O(h2) • O(h3)

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 • 2.0 • 4.0 • 8.0 • 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 • 2.0 • 4.0 • 8.0 • 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 • 0 • 1 • 2 • 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 • 0 • 1 • 2 • 3 10

18. END

19. DISCRETEFUNCTIONS

20. This is what you have been saying about your TI-30Xa • I don't care what people say The rush is worth the priceI pay I get so high when you're with meBut crash and crave you when you are away • Give me back now my TI89Before I start to drink and whine TI30Xa calculators make me cryIncarnation of of Jason will you ever die • TI30Xa – you make me forget the high maintenance TI89. • I never thought I will fall in love again! http://numericalmethods.eng.usf.edu

21. The velocity vs. time is given below. The best estimate of acceleration at t=1.5 in m/s2 is • 83.33 • 128.33 • 173.33 • 183.33

22. The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s2 is • 83.33 • 128.33 • 173.33 • 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 • 36 • 43 • 60 • 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 2nd order polynomial. The best estimate of acceleration at t=1.5 in m/s2 is • 83.33 • 128.33 • 173.33 • 275.00

27. Given y=5e3x + sinx, dy/dx is • 5e3x + cos(x) • 15e3x + cos(x) • 15e3x – cos(x) • 2.666e3x – cos(x)

28. Using forward divided difference with a step size of 0.2, the derivative of f(x)=5e2.3x at x=1.25 is • 258.8 • 163.4 • 211.1 • 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 • 6.697 • 7.389 • 7.438 • 8.179

30. In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E(t), 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.

31. Using forwarded divided difference with a step size of 0.2, the derivative of f(x)=5e2.3x at x=1.25 is • 258.8 • 163.4 • 211.1 • 203.8

33. The exact derivative of f (x)=x 3 at x=5 is most nearly • 25.00 • 75.00 • 106.25 • 125.00 10