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 , z = x z + z y 2 ; P 1 , 2 , − 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 , z = x z + z y 2 ; P 1 , 2 , − 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
,
z
=
x
z
+
z
y
2
;
P
1
,
2
,
−
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.
Suppose a function: R Rhas, at a e R the gradient vector
V (a) = (-6, -2, -20, -7)
Suppose a particle P moves with unit speed through a= (-13,3, 28, 17) with a velocity vector u that makes the angle 4 with Vf(a).
Then what rate of change does P experience at that instant?
Answer
I would need help with a, b, and c as mention below.
(a) Find the gradient of f.(b) Evaluate the gradient at the point P.(c) Find the rate of change of f at P in the direction of the vector u.
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.
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.