E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f ( t ) represent the number of tax returns made through e-file in the year t . ( Source: efile ) Year Number of Tax Returns Made through E-File 2007 80.0 2008 89.9 2009 95.0 2010 98.7 2011 112.2 2012 112.1 2013 114.4 2014 125.8 (a) Find f ( 2014 ) − f ( 2007 ) 2014 − 2007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let t = 7 correspond to 2007. (d) Use the model found in part (c) to complete the table. t 7 8 9 10 11 12 13 14 N (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x = 7 correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f ( t ) represent the number of tax returns made through e-file in the year t . ( Source: efile ) Year Number of Tax Returns Made through E-File 2007 80.0 2008 89.9 2009 95.0 2010 98.7 2011 112.2 2012 112.1 2013 114.4 2014 125.8 (a) Find f ( 2014 ) − f ( 2007 ) 2014 − 2007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let t = 7 correspond to 2007. (d) Use the model found in part (c) to complete the table. t 7 8 9 10 11 12 13 14 N (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x = 7 correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f(t) represent the number of tax returns made through e-file in the year t. (Source: efile)
Year
Number of Tax Returns Made through E-File
2007
80.0
2008
89.9
2009
95.0
2010
98.7
2011
112.2
2012
112.1
2013
114.4
2014
125.8
(a) Find
f
(
2014
)
−
f
(
2007
)
2014
−
2007
and interpret the result in the context of the problem.
(b) Make a scatter plot of the data.
(c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let
t
=
7
correspond to 2007.
(d) Use the model found in part (c) to complete the table.
t
7
8
9
10
11
12
13
14
N
(e) Compare your results from part (d) with the actual data.
(f) Use a graphing utility to find a linear model for the data. Let
x
=
7
correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
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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