For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a . As x → − ∞ , f x → _ _ _ _ _ . b . As x → − 3 − , f x → _ _ _ _ _ . c . As x → − 3 + , f x → _ _ _ _ _ . d . As x → ∞ , f x → _ _ _ _ _ . e . The graph is increasing over the interval s _ _ _ _ _ . f . The graph is decreasing over the interval s _ _ _ _ _ . g . The domain is _ _ _ _ _ . h . The range is _ _ _ _ _ . i . The vaertical asymptote is the line _ _ _ _ _ . j . The horizontal asymptote is the line _ _ _ _ _ .
For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a . As x → − ∞ , f x → _ _ _ _ _ . b . As x → − 3 − , f x → _ _ _ _ _ . c . As x → − 3 + , f x → _ _ _ _ _ . d . As x → ∞ , f x → _ _ _ _ _ . e . The graph is increasing over the interval s _ _ _ _ _ . f . The graph is decreasing over the interval s _ _ _ _ _ . g . The domain is _ _ _ _ _ . h . The range is _ _ _ _ _ . i . The vaertical asymptote is the line _ _ _ _ _ . j . The horizontal asymptote is the line _ _ _ _ _ .
Solution Summary: The author explains how to fill the blanks in the statement with the help of the following graph.
For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1)
a
. As
x
→
−
∞
,
f
x
→
_
_
_
_
_
.
b
. As
x
→
−
3
−
,
f
x
→
_
_
_
_
_
.
c
. As
x
→
−
3
+
,
f
x
→
_
_
_
_
_
.
d
. As
x
→
∞
,
f
x
→
_
_
_
_
_
.
e
. The graph is increasing over the interval
s
_
_
_
_
_
.
f
. The graph is decreasing over the interval
s
_
_
_
_
_
.
g
. The domain is
_
_
_
_
_
.
h
. The range is
_
_
_
_
_
.
i
. The vaertical asymptote is the line
_
_
_
_
_
.
j
. The horizontal asymptote is the line
_
_
_
_
_
.
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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