differentiation a slippery slope - jerks you around - accelerates your mind

DifferentiationA Slippery Slope - Jerks You Around - Accelerates Your Mind

http://nm.mathforcollege.com

Popping tags means

A. Popping bubble wrap

B. Using firecrackers

C. Changing tags of regular items in a store with tags from clearance items

D. Taking illicit drugs

0% 0%0%0%


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


Acceleration of a rocket

tt

v 8.921001014

1014log 2000

4

4

e


2.01BACKGROUND


The definition of the exact derivative of the function f (x) is

1. 2. 3. 4.

25% 25%25%25%A.

B.

C.

D.

x

xfxxfxf

)()(

)('

x

xfxxfxf

)()(

)('

x

xfxxfxf

x

)()(lim)('

0

x

xfxxfxf

x

)()(lim)('

0


Given y=sin(2x), dy/dx at x=3

A. B. C. D.

0% 0%0%0%

A. 0.9600

B. 0.9945

C. 1.920

D. 1.989


END


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. B. C. D.

0% 0%0%0%

A. 11.8

B. 12.0

C. 12.2

D. 36.0


The order of accuracy of the forwarded divided difference approximation

1) O(h)

2) O(h2)

3) O(h3)

33% 33%33%h

xfhxfxf

)()()('


is

The order of accuracy of the central divided difference approximation

1) O(h)

2) O(h2)

3) O(h3)

O(h)

O(h2)

O(h3)

0% 0%0%

h

hxfhxfxf

2

)()()('


is

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.

25% 25%25%25%A. 0

B. 1

C. 2

D. 3

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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

1 2 3 4

25% 25%25%25%

A. 2.0

B. 4.0

C. 8.0

D. 16.0

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END


02.03 DISCRETEFUNCTIONS


The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s2 is

A. B. C. D.

25% 25%25%25%

t (s) 0 0.5 1.1 1.5 1.8

v (m/s) 0 213 223 275 300

A. 83.33

B. 128.33

C. 173.33

D. 183.33


The velocity vs. time is given below. The best estimate of acceleration at t =1.5s in m/s2 is

A. B. C. D.

25% 25%25%25%

t (s) 0 0.5 1.2 1.5 1.8

v (m/s) 0 213 223 275 300

A. 83.33

B. 128.33

C. 173.33

D. 183.33


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

A. B. C. D.

25% 25%25%25%

t (s) 0 0.5 1.2 1.5 1.8

v (m/s) 0 213 223 275 300

A. t=0, 0.5, 1.2

B. t=0.5, 1.2, 1.5

C. t=1.2, 1.5, 1.8

D. t=0, 1.2, 1.8


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.v(t)=-150t2+578.33t-225

1. 2. 3. 4.

25% 25%25%25%

t(s) 0 0.5 1.2 1.5 1.8

v(m/s) 0 213 223 275 300

The best estimate of acceleration at t=1.5 in m/s2 is

A. 83.33

B. 128.33

C. 173.33

D. 275.00


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

Ridt

diLtE )(

1. 2. 3. 4.

25% 25%25%25%

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.

)10.3)(142.0(1.0

10.324.398.0)1(

EA.

B.

C.

D.

10.3*142.0)1( E

)10.3)(142.0(01.0

10.312.398.0)1(

E

1.0

10.312.398.0)1(E


END


differentiation a slippery slope - jerks you around - accelerates your mind

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