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

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

2. Oil Spill http://nm.mathforcollege.com

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

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

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

6. The definition of the exact derivative of the function f (x) is 10 http://nm.mathforcollege.com

7. The exact derivative of f (x)=x 3 at x=5 is most nearly • 25.00 • 75.00 • 106.25 • 125.00 10 http://nm.mathforcollege.com

8. Given y=5e3x + sinx, dy/dx is • 5e3x + cos(x) • 15e3x + cos(x) • 15e3x – cos(x) • 2.666e3x – cos(x) http://nm.mathforcollege.com

9. Given y=sin(2x), dy/dx at x=3 • 0.9600 • 0.9945 • 1.920 • 1.989 10 http://nm.mathforcollege.com

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

12. 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 http://nm.mathforcollege.com

13. 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 http://nm.mathforcollege.com

14. The order of accuracy of the forwarded divided difference approximation • O(h) • O(h2) • O(h3) is http://nm.mathforcollege.com

15. 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 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 • 2.0 • 4.0 • 8.0 • 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 • 0 • 1 • 2 • 3 10 http://nm.mathforcollege.com

18. The order of accuracy of the central divided difference approximation • O(h) • O(h2) • O(h3) is http://nm.mathforcollege.com

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 • 2.0 • 4.0 • 8.0 • 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 • 36 • 43 • 60 • Cannot be found http://nm.mathforcollege.com

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22. 02.03 DISCRETEFUNCTIONS http://nm.mathforcollege.com

23. 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 http://nm.mathforcollege.com

24. 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 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=0, 0.5, 1.2 • t=0.5, 1.2, 1.3 • t=1.2, 1.3, 1.4 • 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 2nd order polynomial. The best estimate of acceleration at t=1.5 in m/s2 is • 83.33 • 128.33 • 173.33 • 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), If L=0.98 henries and R=0.142 ohms, find E(1.00) with most accuracy and choosing amongst FDD, BDD or CDD. http://nm.mathforcollege.com

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