Differentiation A Slippery Slope Jerks You Around Accelerates

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

Oil Spill Time (s ) 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 3. 5 4. 0 4. 5 5. 0 Radius(m ) 0 0. 236 0. 667 1. 225 1. 886 2. 635 3. 464 4. 365 5. 333 6. 364 7. 454 http: //nm. mathforcollege. com

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

2. 01 BACKGROUND http: //nm. mathforcollege. com

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

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

The exact derivative of f (x)=x 3 at x=5 is most nearly A. B. C. D. 25. 00 75. 00 106. 25 125. 00 http: //nm. mathforcollege. com

Given y=5 e 3 x + sinx, dy/dx is 1. 2. 3. 4. 5 e 3 x + cos(x) 15 e 3 x – cos(x) 2. 666 e 3 x – cos(x) http: //nm. mathforcollege. com

Given y=sin(2 x), dy/dx at x=3 A. B. C. D. 0. 9600 0. 9945 1. 920 1. 989 http: //nm. mathforcollege. com

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02. 02 CONTINUOUS FUNCTIONS http: //nm. mathforcollege. com

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

Using forwarded divided difference with a step size of 0. 2, the derivative of f(x)=5 e 2. 3 x at x=1. 25 is A. B. C. D. 258. 8 163. 4 211. 1 203. 8 http: //nm. mathforcollege. com

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

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

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. B. C. D. 2. 0 4. 0 8. 0 16. 0 http: //nm. mathforcollege. com 10

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

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

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. B. C. D. 2. 0 4. 0 8. 0 16. 0 http: //nm. mathforcollege. com 10

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. 2. 3. 4. 36 43 60 Cannot be found http: //nm. mathforcollege. com

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02. 03 DISCRETE FUNCTIONS http: //nm. mathforcollege. com

The velocity vs. time is given below. The best estimate of acceleration at t =1. 5 s in m/s 2 is t (s) 0 0. 5 1. 1 1. 5 1. 8 v (m/s) 0 213 223 275 300 A. B. C. D. 83. 33 128. 33 173. 33 183. 33 http: //nm. mathforcollege. com

The velocity vs. time is given below. The best estimate of acceleration at t =1. 5 s in m/s 2 is t (s) 0 0. 5 1. 2 1. 5 1. 8 v (m/s) 0 213 223 275 300 A. B. C. D. 83. 33 128. 33 173. 33 183. 33 http: //nm. mathforcollege. com

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. 1 s are t (s) 0 0. 5 1. 2 1. 5 1. 8 v (m/s) 0 213 223 275 300 A. B. C. D. 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

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. The best estimate of acceleration at t=1. 5 in m/s 2 is t(s) 0 v(m/s) 0 A. B. C. D. 0. 5 213 1. 2 223 1. 5 275 1. 8 300 83. 33 128. 33 173. 33 275. 00 http: //nm. mathforcollege. com

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. 00 1. 01 1. 03 1. 1 Current, i (amperes) 3. 10 3. 12 3. 18 3. 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

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