Post on 03-Jan-2016
DifferentiationA Slippery Slope - Jerks You Around - Accelerates Your Mind
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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%
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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
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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
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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
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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
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The order of accuracy of the forwarded divided difference approximation
1) O(h)
2) O(h2)
3) O(h3)
33% 33%33%h
xfhxfxf
)()()('
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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
)()()('
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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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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
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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
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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
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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
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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
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