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nature of mathematics

Questions and Answers of Nature Of Mathematics

Apportion the scholarships using Hamilton's method.Each year, 100 scholarships are awarded to the students. Use this information in Problems 33-36. A university has two colleges, Letters and Sciences
Decide if the Alabama paradox occurs if the number of scholarships is increased from 100 to 101.Each year, 100 scholarships are awarded to the students. Use this information in Problems 33-36. A
Suppose that a third Professional \((\mathrm{P})\) college is established with 525 students. Also, assume that 5 new scholarships are established. Use Hamilton's method to apportion the 105
Does the new states paradox occur in Problem 35?Data from Problem 35Suppose that a third Professional \((\mathrm{P})\) college is established with 525 students. Also, assume that 5 new scholarships
An election with three candidates has the following rankings:a. Is there a majority? If not, who wins the plurality vote?b. Who wins using the Borda count method?c. Does the Borda method violate the
What is the Pareto principle?
The city of St. Louis, Missouri, passed a ballot measure to provide and pay for 180 surveillance cameras for high-crime areas. The city council mandated that these cameras be apportioned among the
Consider the sequence \(0.4,0.44,0.444,0.4444, \cdots\). What do you think is the appropriate limit of this sequence?
Write out the first five terms (beginning with \(n=1\) ) of the sequences given in Problems 3-10.\(\left\{\left(\frac{1}{3}ight)^{n-1}ight\}\) \(1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27},
The graph in Figure 18.19 shows the height h of a projectile after \(t\) seconds. In Problems 5-8, find the average rate of change of height (in feet) with respect to the requested changes in time
Evaluate the area function for the functions given in Problems 1-8.Let \(y=3 x+2\); find \(A(3)\).
Evaluate the limits in Problems 3-7.\(\lim _{n ightarrow \infty}(2 n+3)\)
Consider the sequence \(0.5,0.55,0.555,0.5555, \cdots\). What do you think is the appropriate limit of this sequence?
The graph in Figure18.19 shows the height h of a projectile after \(t\) seconds. In Problems 5-8, find the average rate of change of height (in feet) with respect to the requested changes in time
Write out the first five terms (beginning with \(n=1\) ) of the sequences given in Problems 3-10.\(\left\{\frac{3 n+1}{n+2}ight\}\)
Evaluate the limits in Problems 3-7.\(\lim _{n ightarrow \infty}\left(1+\frac{1}{n}ight)^{n}\)
Evaluate the area function for the functions given in Problems 1-8.Let \(y=5-2 x\); find \(A(2)\).
Consider the sequence \(6,6.6,6.66,6.666, \cdots\). What do you think is the appropriate limit of this sequence?
Write out the first five terms (beginning with \(n=1\) ) of the sequences given in Problems 3-10.\(\left\{\frac{2 n-1}{n+1}ight\}\)
The graph in Figure 18.19 shows the height h of a projectile after \(t\) seconds. In Problems 5-8, find the average rate of change of height (in feet) with respect to the requested changes in time
Evaluate the area function for the functions given in Problems 1-8.Let \(y=x+5\); find \(A(x)\).
Use the definition of derivative to find the derivatives in Problems 8-12.\(f(x)=9\)
Consider the sequence \(0.9,0.99,0.999,0.9999, \cdots\). What do you think is the appropriate limit of this sequence?
Write out the first five terms (beginning with \(n=1\) ) of the sequences given in Problems 3-10.\(\left\{\frac{n^{2}+n}{2-n^{2}}ight\}\)
Find the antiderivative by using areas in Problems 9-22.\(\int 6 d x \)
The graph in Figure 18.20 shows company output as a function of the number of workers. In Problems 9-12, find the average rate of change of output for the given change in the number of
Use the definition of derivative to find the derivatives in Problems 8-12.\(f(x)=10-2 x-2\)
Consider the sequence \(0.27,0.2727,0.272727, \cdots\). What do you think is the appropriate limit of this sequence?
Write out the first five terms (beginning with \(n=1\) ) of the sequences given in Problems 3-10.\(\left\{\frac{n^{2}-n}{n^{2}+n}ight\}\)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. d
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.212009
Find the antiderivative by using areas in Problems 9-22.\(\int(5+x) d x\)
Evaluate the integrals in Problems 15-17.\(\int_{0}^{2}\left(x-3 x^{2}ight) d x\)
Find the antiderivative by using areas in Problems 9-22.\(\int 3 d x \)
The graph in Figure 18.20 shows company output as a function of the number of workers. In Problems 9-12, find the average rate of change of output for the given change in the number of
Use the definition of derivative to find the derivatives in Problems 8-12.\(f(x)=x-10\)
Consider the sequence \(0.36,0.3636,0.363636, \cdots\). What do you think is the appropriate limit of this sequence?
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{8,000 n}{n+1}\)
Find the antiderivative by using areas in Problems 9-22.\(\int 5 d x \)
The graph in Figure 18.20 shows company output as a function of the number of workers. In Problems 9-12, find the average rate of change of output for the given change in the number of
Use the definition of derivative to find the derivatives in Problems 8-12.\(f(x)=6-4 x^{2}-8 x\)
Consider the sequence \(3,3.1,3.14,3.141,3.1415,3.14159\), \(3.141592, \cdots\). What do you think is the appropriate limit of this sequence?
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{8,000}{n-1}\)
Find the antiderivative by using areas in Problems 9-22.\(\int d x\)
The graph in Figure 18.20 shows company output as a function of the number of workers. In Problems 9-12, find the average rate of change of output for the given change in the number of
Use the definition of derivative to find the derivatives in Problems 8-12.\(f(x)=44 e^{0.5 x}\)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. O P
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{n}{n-5,000}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(x+5) d x\)
The SAT scores of entering first-year college students are shown in Figure18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.212006 to
Find the antiderivative in Problems 13-14.\(\int 16 x d x \)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. O P
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{n}{5,000-n}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(x+6) d x\)
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.212007
Find the antiderivative in Problems 13-14.\(\int \pi d x \)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. P X
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{2 n+1}{3 n-4}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(3+x) d x\)
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.212008
Evaluate the integrals in Problems 15-17.\(\int_{2}^{3}\left(6 x^{2}-2 xight) d x \)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. P X
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{3 n-1}{1-2 n}\)
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{4 n-1}{3 n+10}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(3 x+4) d x\)
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.212010
Evaluate the integrals in Problems 15-17.\(\int_{1}^{2} e^{x} d x\) (correct to two decimal places)
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. P
Find each limit in Problems 11-18, if it exists.\(\lim _{n ightarrow \infty} \frac{4-7 n}{8+n}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(2 x+5) d x\)
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods.Figure 18.21What
Find the equation of the line tangent to \(y=x^{2}\) at \(x=1\).
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. d
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{5 n+8}{n}ight\}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(1+8 x) d x\)
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{5 n}{n+7}ight\}\)
Find the antiderivative by using areas in Problems 9-22.\(\int(4 x+3) d x\)
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{n+1}{n+2}\)
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{8 n^{2}+800 n+5,000}{2 n^{2}-1,000 n+2}ight\}\)
What is a derivative?
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{1}{2 n}\)
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{100 n^{2}+7,000}{n^{2}-n-1}ight\}\)
What is an integral?
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{4-n}{n+1}\)
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{8 n^{2}+6 n+4,000}{n^{3}+1}ight\}\)
What is the area function?
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{1-n}{n+10}\)
Compute the limit of the convergent sequences in Problems 19-26.\(\left\{\frac{8 n^{3}-6 n^{2}+85}{2 n^{3}-5 n+170}ight\}\)
Contrast a definite integral and an indefinite integral.
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{1}{n}\)
Graph each sequence in Problems 27-34 in one dimension.\(a_{n}=\frac{1}{n}\)
Show that \(x^{2}\) is an antiderivative of \(2 x\).
Trace the curves in Problems 27-32 onto your own paper and draw the secant line passing through \(P\) and \(Q\). Next, imagine \(h ightarrow 0\) and draw the tangent line at \(P\) assuming that \(Q\)
In Problems 21-38, guess the requested limits.\(\lim _{n ightarrow \infty} \frac{100}{n}\)
Table 18.5 shows the gross national product (GNP) in trillions of dollars for the years 1960-2012. Find the average yearly rate of change of the GNP for the requested years in Problems

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