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

Oil Spill Time (s ) Radius(m )

Acceleration of a rocket

2.01 BACKGROUND

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

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

The exact derivative of f (x)=x 3 at x=5 is most nearly A B C D

Given y=5e 3x + sinx, dy/dx is 1. 5e 3x + cos(x) 2. 15e 3x + cos(x) 3. 15e 3x – cos(x) e 3x – cos(x)

Given y=sin(2x), dy/dx at x=3 A B C D

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02.02 CONTINUOUS FUNCTIONS

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

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 B C D

The order of accuracy of the forwarded divided difference approximation 1)O(h) 2)O(h 2 ) 3)O(h 3 ) is

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

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

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

The order of accuracy of the central divided difference approximation 1)O(h) 2)O(h 2 ) 3)O(h 3 ) is

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

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 Cannot be found

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02.03 DISCRETE FUNCTIONS

The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s 2 is t (s) v (m/s) A B C D

The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s 2 is t (s) v (m/s) A B C D

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) v (m/s) 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

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) v(m/s) The best estimate of acceleration at t=1.5 in m/s 2 is A B C D

In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E(t), Time, t (secs) Current, i (amperes) 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.

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