For Exercises 61-68, perform the indicated operations for the given vectors. (See Example 6) v = − 3.3 i + 11 j w = 4 i + j s = 7.2 i − 5.4 j r = − 12 i − 5 j s - r
For Exercises 61-68, perform the indicated operations for the given vectors. (See Example 6) v = − 3.3 i + 11 j w = 4 i + j s = 7.2 i − 5.4 j r = − 12 i − 5 j s - r
Solution Summary: The author calculates the value of s-r based on the given vector.
For Exercises 61-68, perform the indicated operations for the given vectors. (See Example 6)
v
=
−
3.3
i
+
11
j
w
=
4
i
+
j
s
=
7.2
i
−
5.4
j
r
=
−
12
i
−
5
j
s
-
r
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.
Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)
Q1:
A slider in a machine moves along a fixed straight rod. Its
distance x cm along the rod is given below for various values of the time. Find the
velocity and acceleration of the slider when t = 0.3 seconds.
t(seconds)
x(cm)
0 0.1 0.2 0.3 0.4 0.5 0.6
30.13 31.62 32.87 33.64 33.95 33.81 33.24
Q2:
Using the Runge-Kutta method of fourth order, solve for y atr = 1.2,
From
dy_2xy +et
=
dx x²+xc*
Take h=0.2.
given x = 1, y = 0
Q3:Approximate the solution of the following equation
using finite difference method.
ly -(1-y=
y = x), y(1) = 2 and y(3) = −1
On the interval (1≤x≤3).(taking h=0.5).
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
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