Find a unit vector in the direction in which f increases most rapidly at P , and find the rate of change of f at P in that direction. f x , y = x x + y ; P 0 , 2
Find a unit vector in the direction in which f increases most rapidly at P , and find the rate of change of f at P in that direction. f x , y = x x + y ; P 0 , 2
Find a unit vector in the direction in which
f
increases most rapidly at
P
,
and find the rate of change of
f
at
P
in that direction.
f
x
,
y
=
x
x
+
y
;
P
0
,
2
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
F- 02. The following data was collected for the distance traveled versus time for a rocket:
t,s
Y, km
25
50
75
100
125
32
58
78
92
100
Use numerical differentiation to estimate the rocket's velocity and acceleration at each
time.
Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional
to the current i flowing through the resistor as V= iR. Where R is the resistance. However,
real resistors may not always obey Ohm's law. Suppose that you perform some very
precise experiments to measure the voltage drop and the corresponding current for a
resistor. The following results suggest a curvilinear relationship rather than the straight
line represented by Ohm's law.
i
-1
- 0.5
- 0.25
0.25
0.5
1
V
-637
-96.5
-20.25
20.5
96.5
637
Instead of the typical linear regression method for analyzing such experimental data, fit a
curve to the data to quantify the relationship. Compute V for i = 0.1 using Polynomial
Interpolation.
Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional
to the current i flowing through the resistor as V= iR. Where R is the resistance. However,
real resistors may not always obey Ohm's law. Suppose that you perform some very
precise experiments to measure the voltage drop and the corresponding current for a
resistor. The following results suggest a curvilinear relationship rather than the straight
line represented by Ohm's law.
i
-1
- 0.5
- 0.25
0.25
0.5
1
V
-637
-96.5
-20.25
20.5
96.5
637
Instead of the typical linear regression method for analyzing such experimental data, fit a
curve to the data to quantify the relationship. Compute V for i = 0.1 using Newton's
Divided Difference Method.
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