Determine whether the series is convergent or divergent. 00 ke-12 k=1
Find a power series representation for the function and determine the radius of convergence. f(x) = x 2 tan 1 (x 3 )
Use the Integral Test to determine whether the series is convergent or divergent. A=2 1 n(In n)3
List the first five terms of the sequence. an (-1)" 4"
The position (in meters) of a particle at time t seconds is given by the parametric equations (a) Find the speed of the particle at the point (6, 4). (b) What is the average speed of the particle for...
Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. x = 2 t t, y = 2 t + t, 3 t 3
Suppose you know that the series converges for |x| < 2. What can you say about the following series? Why? =o bnx" n=0
Taking a cruise is a costly discretionary expense. In a recent year, the top five cruise lines in the world had this many passengers: Round your answers to the nearest integer. a. The computations...
In each of the equations below, t represents the term of a savings account. Find the value of t to the nearest tenth of a year. a. b. c. d. e. t= log1.03 (1.975) 12
Chris purchases living room furniture for $4,345 from Halloran Gallery. She has a 1-year, no-interest, no-money-down, deferred payment plan. She does have to make a $15 monthly payment for the first...
Suppose Britta only paid the interest during her 2 years in school and the 6-month grace period. What will she pay in interest over the term of her loan? Britta has been accepted into a 2-year...
Arrange the following lending institutions in descending order according to their APRs for a $10,000, 2-year loan. East Meadow Savings 4 1/2% Clinton Park Credit Union 4% Tivoli Trust 4 3/8% First...
Dylan purchased A points, each of which reduced his APR by B%. The cost per point was 1% of the loan amount. His new APR is C%, and his points cost him D dollars. Write an algebraic expression for:...
The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. The Glen Head Boys Club built a ramp for a local school. The dimensions of the ramp...
Keisha is purchasing an apartment for $180,000. She has been approved for a 4.0% mortgage. She put 10% down and will be closing on April 22. Her first payment is due May 1. How much should she expect...
What is the difference between the days high and low prices for McDonalds Corp?
Van Siclen Farms plants only corn and soybeans on their 4,000-acre fields. The corn yields a profit of $160 per acre, and the soybean profit is $340 per acre. This year the owners have decided to...
A corporation produces mini-widgets. The variable expenses are $1.24 per mini-widget, and the fixed expenses are $142,900. a. What is the total cost to produce one mini-widget? b. What is the total...
Determine and sketch or graph the sets in the complex plane given by < |z - 4 + 2i| < 3
Let a = [1, -3, 5], b = [4, 0, 8], c = [-2, 9, 1]. Find: 5a 13b, 65a b
Find a parametric representation Circle in the plane z = 1 with center (3, 2) and passing through the origin.
Find all the singularities in the finite plane and the corresponding residues. Show the details. cot z
Can we conclude from Example 4 that the integral is also zero over the contour in Prob. 1? Data from Prob. 1 Verify Theorem 1 for the integral of over the boundary of the square with vertices 1 i....
Find all c Z 3 such that Z 3 [x]/(x 3 + cx 2 + 1) is a field.
Show that is a subfield of R by using the ideas of this section, rather than by a formal verification of the field axioms. {a + b(2) + c(2) a, b, c = Q}
Let E be an extension field of F, and let , E. Suppose is transcendental over F but algebraic over F(). Show that is algebraic over F().
Find the degree and a basis for the given field extension. Be prepared to justify your answers. Q(2 + 3) over Q
Let us consider Z[x]. a. Is Z[x] a UFD? Why? b. Show that {a + xf(x)|a 2Z, f(x) Z[x]} is an ideal in Z[x]. c. Is Z[x] a PID? (Consider part (b).) d. Is Z[x] a Euclidean domain? Why?
Let a be algebraic of degree n over F. Show from Corollary 48 .5 that there are at most n different isomorphisms of F() onto a subfield of F and leaving F fixed. Data from Corollary 48.5 Let be...
Calculate the perimeter and area of each of these rectangles of length l and breadth b. Write the units of your answers clearly. a. l = 4cm, b = 7 cm b. l = 8cm, b = 12cm c. l = 4.5 cm, b = 2 cm d. l...
Write an expression for the area of each of the following shapes. a. b. 8 j -j- 3
At a Cambridge college, 65% of the maths students come from England. If there are 240 maths students, how many are not from England?
A circle passes through the points O(0, 0), P(3, 9) and Q(11, 11). Find the equation of the circle.
Find the equation of the circle that passes through the points (7, 3) and (11, 1) and has its centre lying on the line 2x + y = 7.
We are given m data points and we seek an hyperplane where and that best fits the given points, in the sense of a minimum sum of squared distances criterion. Formally, we need to solve the...
Find the centre and the radius of each of the following circles. a. x 2 + y2 = 16 b. 2x 2 + 2y2 = 9 c. x 2 + (y 2) 2 = 25 d. (x 5) 2 + (y + 3) 2 = 4 e. (x + 7) 2 + y 2 = 18 f. 2(x 3) 2 + 2(y + 4)...
Paint is poured onto a flat surface and a circular patch is formed. The area of the patch increases at a rate of 5cm 2 s 1 . a. Find, in terms of , the radius of the patch after 8 seconds. b. Find,...
A company buys a machine for $475,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. What is its value after 5 years?
The diagram shows a water container in the shape of a triangular prism of length 120 cm. The vertical cross-section is an equilateral triangle. Water is poured into the container at a rate of 24 cm 3...
A demolition ball is used to tear down a building. Its distance s (in m) above the ground as a function of time t (in s) after it is dropped is s = 17.5 4.9t 2 . Because s = f (t), find f(1.2).
Use Figure 2.19 to fill in the blanks in the following statements about the function f at point A. (a) f(_ ) = ___ (b) f'(_ ) = ___ (7,3) (7.2.3.8) Figure 2.19 Tangent line f(x)
Use a calculator or computer to evaluate the integral. 3 4 Ve + zdz
With t in seconds, the velocity of an object is v(t) = 10 + 8t t 2 m/sec. (a) Represent the distance traveled during the first 5 seconds as a definite integral and as an area. (b) Estimate the...
Figure 5.9 shows the velocity of an object for 0 t 6. Calculate the following estimates of the distance the object travels between t = 0 and t = 6, and indicate whether each result is an upper or...
Assume points P and Q are close. Estimate g(Q). P = (30, 125), Q = (25, 135), g(P) = 840, g x (P) = 4,g y (P) = 1.5.
Find a possible formula for the function represented by the data. x 0 f(x) 4.30 1 2 6.02 8.43 3 11.80
Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y) = x 2 + y 2
Find the derivative of the functions in Problems. f(x) = 6e 5x + e x2
The vase in Figure 4.31 is filled with water at a constant rate (that is, constant volume per unit time). (a) Graph y = f(t), the depth of the water, against time, t. Show on your graph the points at...
The function f is defined for all x. Use the graph of f' to decide: (a) Over what intervals is f increasing? Decreasing? (b) Does f have local maxima or minima? If so, which, and where? 2 f'(x) 4 X
The function f is defined for all x. Use the graph of f' to decide: (a) Over what intervals is f increasing? Decreasing? (b) Does f have local maxima or minima? If so, which, and where? -1 f'(x) x
For what values of a and b does f(x) = a(x b ln x) have a local minimum at the point (2, 5)? Figure 4.16 shows a graph of f(x) with a = 1 and b = 1. 3 2 1 f(x) = x-lnx 1 2 Figure 4.16 3 X
Let F(x) be an antiderivative of f(x), with F(0) = 50 and 5 0 f(x) dx = 12. What is F(5)?
Table 6.2 shows the monthly change in water stored in Lake Sonoma, California, from March through November 2014. The change is measured in acre-feet per month.1 On March 1, the water stored was...
Find the derivative of the functions in Problems. R = (q 2 + 1) 4
Use the tangent line approximation. Given f(x) = x 4 x 2 + 3 approximate f(1.04).
Use the tangent line approximation. Given f(x) = x 3 + x 2 6, approximate f(0.97).
For the functions in Problems (a) Find the derivative at x = 1. (b) Find the second derivative at x = 1. (c) Use your answers to parts (a) and (b) to match the function to one of the graphs in Figure...
For f(x) = x 2 + 5x +2, find the equation of the tangent line at (a) x = 1 (b) x = 1
(a) Find the equation of the tangent line to f(x) = x 3 at the point where x = 2. (b) Graph the tangent line and the function on the same axes. If the tangent line is used to estimate values of the...
Fill in each blank so that the resulting statement is true. When solving by the addition method, we can eliminate y by multiplying the first equation by 2 and the second equation by________ , and...
Identify a piece of information that you have gained through each of the sources of knowledge discussed in this chapter (superstition and intuition, authority, tenacity, rationalism, empiricism, and...
Organize the data in Exercise 1 into a class interval frequency distribution using 10 intervals with frequency (f) and relative frequency (rf) columns. s8
For the distribution described in exercise 4, what is the probability of selecting someone who is 70 inches or taller or 64 inches or shorter? Data from exercise 4 If height is normally distributed...
In a study on caffeine and stress, college students indicated how many cups of coffee they drink per day and their stress level on a scale of 1 to 10. The data are provided in the following table....
A researcher is interested in whether students who attend private high schools have higher average SAT scores than students in the general population. A random sample of 90 students at a private high...
What is the advantage of manipulating more than one independent variable in an experiment?
A researcher interested in the effects of exercise on stress had participants exercise for 30, 60, or 90 minutes per day. The mean stress level on a 100-point stress scale (with 100 indicating high...
What is the difference between a between- groups research design and a within-groups research design?
What is the geometric mean of LVMI by blood pressure group?
The following statements are wrong but can be corrected by substituting one word or phrase. (See the instructions in Exercise 1.13.) Identify the incorrect word or phrase in each of the following...
Orthostatic hypertension is sometimes defined based on an unusual change in blood pressure after changing position. Suppose we define a normal range for change in systolic blood pressure (SBP) based...
German psychologist David Loschelder and his colleagues conducted an experiment on negotiations (2014). They cited tennis player Andy Roddicks agent who thought it was always detrimental to make an...
For each variable (other than ID), obtain appropriate descriptive statistics (both numeric and graphic)? Table 2.17: Format for FEV.DAT The data in Table 2.17 are available for each child. Variable...
What is the expected overall CHD mortality rate in Olmstead County in 2015 if these trends continue? The investigators reported that for both men and women, inhospital CHD death rates were declining...
To assess the variability of the assay, the investigators need to compute the coefficient of variation. Compute the coefficient of variation (CV) for each subject by obtaining the mean and standard...
Suppose 6 of 15 students in a grade-school class develop influenza, whereas 20% of grade-school students nationwide develop influenza. Is there evidence of an excessive number of cases in the class?...
Suppose we know two of the three people have Alzheimers disease. What is the conditional probability that they are both younger than 80 years of age? Mental Health Estimates of the prevalence of...
What is the conditional probability that the woman will be affected given that the man is affected? How does this value compare with the prevalence in Table 3.5? Why should it be the same (or...
What is the probability that at least one member of the couple is affected? Suppose the probability that both members of a married couple, each of whom is 7579 years of age, will have Alzheimers...
What is the probability of obtaining exactly 6 events for a Poisson distribution with parameter = 4.0? Suppose we want to check the accuracy of self-reported diagnoses of angina by getting further...
Find the probability of getting 3 or more episodes of otitis media in the first 2 years of life. Otolaryngology Assume the number of episodes per year of otitis media, a common disease of the middle...
Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? Infectious Disease Commonly used...
If A, B are two events such that A = {older child is affected}, B = {younger child is affected}, then are the events A, B independent? Genetics Suppose that a disease is inherited via a dominant mode...
Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from...
What is the probability that 0 rats will die in the 8-hour period? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a...
What is the PV of the test? Suppose the self-reports are completely accurate and are representative of the number of eighth-grade students who smoke in the general community. We are considering using...
After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time? Ophthalmology,...
A sample of 504 patients in early stages of Alzheimers disease is divided into two groups. One group receives an experimental drug; the other receives a placebo. The advance of the disease in the...
A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant? A research objective is presented. For each, identify the population and...
What is the sensitivity of the test? Mental Health The Chinese Mini-Mental Status Test (CMMS) consists of 114 items intended to identify people with Alzheimers disease and senile dementia among...
To determine the prevalence of human growth hormone (HGH) use among high school varsity baseball players, the State Athletic Commission randomly selects 50 high schools. All members of the selected...
A college official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a simple random sample from each class and asks the...
To obtain students opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one...
What is the probability of 0, 1, and 2+ additional pregnancies if the first birth was a stillbirth? Demography A study based on data collected from the Medical Birth Registry of Norway looked at...
The county sheriff wants to determine if a certain highway has a high proportion of speeders traveling on it. Design a sampling method to obtain the individuals in the sample. Be sure to support your...
When should relative frequencies be used when comparing two data sets? Why?
What is the probability that exactly two of the two offspring will be affected in a family with dominant disease with complete penetrance? Genetics A dominantly inherited genetic disease is...
The following data represent the number of grams of fat in breakfast meals offered at McDonalds. (a) construct a stem-and-leaf plot and (b) describe the shape of the distribution. 27 25 30 32 12 22...
Why shouldnt classes overlap when summarizing continuous data in a frequency or relative frequency distribution?