Question: Explain why each function is continuous or

> Most people who commit fraud feel a perceived financial pressure.

> Because of the nature of fraud, auditors are often in the best position to detect its occurrence.

> Fraud is a crime that is seldom observed.

> A single symptom (red flag) is almost always enough information to identify the type of fraud scheme occurring.

> The z-score calculation is the best way to stratify data.

> Vertical analysis is a useful detection technique because percentages are easily understood.

> Vertical analysis is a more direct method than horizontal analysis in focusing on changes in financial statements from one period to another.

> Balance sheets must be converted to change statements before they can be used in detecting fraud.

> Unusual patterns always indicate the existence of fraud.

> First-time offenders usually exhibit no psychological changes.

> The Gramm-Leach-Bliley Act of 1999 made it more difficult for officials and private citizens to access information from financial institutions.

> As fraud perpetrators become more confident in their fraud schemes, they usually steal and spend increasingly larger amounts.

> Most people who commit fraud use the embezzled funds to save for retirement.

> Analytical fraud symptoms are the least effective way to detect fraud.

> The internal control system of an organization is comprised of the control environment, the accounting system, and control procedures (activities).

> Internal control weaknesses give employees opportunities to commit fraud.

> A check is an example of a source document.

> Recording an expense is a possible way to conceal the theft of cash.

> Some complaints and tips turn out to be unjustified.

> Auditors can best help detect fraud at the conversion stage.

> The three elements of a typical fraud consist of concealment, conversion, and completion.

> Conversion is the third element of the fraud investigation triangle.

> It is safe to assume that fraud has not occurred if one or more elements of the fraud triangle cannot be observed.

> Psychopaths feel no guilt because they have no conscience.

> Analytical anomalies are present in every fraud.

> The increasingly complex nature of business helps to decrease the number of collusive frauds.

> Even a good system of internal controls will often not be completely effective because of fallibilities of the people applying and enforcing the controls.

> Not prosecuting fraud perpetrators is cost-effective both in the short run and the long run.

> The two elements in creating a positive work environment are (1) having an open-door policy and (2) having positive personnel and operating procedures.

> When fraud is committed, the problem is often not a lack of controls, but the overriding of existing controls by management and others.

> A good internal control system within a company can ensure the absence of fraud.

> An important factor in creating a culture of honesty, openness, and assistance in the workplace is maintaining an employee assistance program.

> For various reasons, the net worth method tends to be a conservative estimate of amounts stolen.

> Perpetrators usually save what they steal.

> The ellipsoid 4x2 + 2y2 + z2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

> The paraboloid z = 6 - x - x2 - 2y2 intersects the plane x = 1 in a parabola. Find parametric equations for the tangent line to this parabola at the point (1, 2, -4). Use a computer to graph the paraboloid, the parabola, and the tangent line on the same

> You are told that there is a function f whose partial derivatives are fx (x, y) = x + 4y and fy (x, y) = 3x - y. Should you believe it?

> A contour map is given for a function f. Use it to estimate fx (2, 1) and fy (2, 1). -3 6. -2 10 12 14. 2 16 3 18

> The following surfaces, labeled a, b, and c, are graphs of a function f and its partial derivatives fx and fy. Identify each surface and give reasons for your choices. 8 4 -4 a -8 -2 -3 -2 -1 0 1 2 y 2. 3. 4 -4 -3 -2 -1 0 1 3 y -4 -8- -2 -3 -2 -1 0

> The average energy E (in kcal) needed for a lizard to walk or run a distance of 1 km has been modeled by the equation where m is the body mass of the lizard (in grams) and v is its speed (in km/h). Calculate Em (400, 8) and Ev (400, 8) and interpret y

> A model for the surface area of a human body is given by the function S = f (w, h) = 0.1091w0.425h0.725 where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. Calculate and interpret the partial derivatives.

> Find the limit, if it exists, or show that the limit does not exist. ху lim (x y-0, 0) Vx2 + y?

> Let g (x, y) = cos (x + 2y). (a). Evaluate g (2, -1). (b). Find the domain of g. (c). Find the range of g.

> Find the limit, if it exists, or show that the limit does not exist. 5y cos?x lim (x, y)(0, 0) x + y* 4

> Find the limit, if it exists, or show that the limit does not exist. x* – 4y? lim (x, y (0, 0) x? + 2y?

> Find the limit, if it exists, or show that the limit does not exist. lim (x, y)- (3, 2) evzi-y

> Find the limit, if it exists, or show that the limit does not exist. lim (x, y)- (m, w/2) y sin(x – y)

> Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as (x, y) → (0, 0). Then explain why your guess is correct. 2ху f(x, y) = x² + 2y²

> Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f (x, y) as (x, y) → (0, 0). Then explain why your guess is correct. x*y* + x*y* ² – 5 2 f(x, y) = 2 - xy

> Suppose that lim (x, y) → (3, 1) f (x, y) = 6. What can you say about the value of f (3, 1)? What if f is continuous?

> Graph the functions In general, if t is a function of one variable, how is the graph of obtained from the graph of t? f(x, y) = /x² + y² f(x, y) = evya f(x, y) = Inx? + y2 f(x, y) = sin(/r? + y² 1 f(x, y) x² + y? f(x, y) = 9(Vx² + y?)

> Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified value of t. r(t) = t i + 2 cos t j + sin t k, t = 0

> Use a computer to investigate the family of surfaces z = x2 + y2 + cxy. In particular, you should determine the transitional values of c for which the surface changes from one type of quadric surface to another.

> Use a computer to investigate the family of surfaces z = (ax2 + by2) e-x2-y2 How does the shape of the graph depend on the numbers a and b?

> Investigate the family of functions f (x, y) = ecx2+y2. How does the shape of the graph depend on c?

> Graph the function using various domains and viewpoints. Comment on the limiting behavior of the function. What happens as both x and y become large? What happens as (x, y) approaches the origin? f(x, y) x? + y?

> Graph the function using various domains and viewpoints. Comment on the limiting behavior of the function. What happens as both x and y become large? What happens as (x, y) approaches the origin? x + y f(x, y) = x? + y?

> Use a computer to graph the function using various domains and viewpoints. Get a printout that gives a good view of the “peaks and valleys.” Would you say the function has a maximum value? Can you identify any points on the graph that you might consider

> Use a computer to graph the function using various domains and viewpoints. Get a printout that gives a good view of the “peaks and valleys.” Would you say the function has a maximum value? Can you identify any points on the graph that you might consider

> Describe how the graph of g is obtained from the graph of f. (a). t (x, y) = f (x - 2, y) (b). t (x, y) = f (x, y + 2) (c). t (x, y) = f (x + 3, y – 4)

> Describe how the graph of g is obtained from the graph of f . (a). t (x, y) = f (x, y) + 2 (b). t (x, y) = 2f (x, y) (c). t (x, y) = -f (x, y) (d). t (x, y) = 2 - f (x, y)

> Describe the level surfaces of the function. f (x, y, z) = x2 - y2 - z2

> Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified value of t. r(t) = t i + t2 j + 2 k, t = 1

> If c ∈ Vn, show that the function f given by f (x) = c ∙ x is continuous on Rn.

> Show that the function f given by f (x) = |x | is continuous on Rn. [Hint: Consider |x - a |2 = (x – a) ∙ (x – a).]

> Let (a). Show that f (x, y) → 0 as (x, y) → (0, 0) along any path through s0, 0d of the form y = mxu with 0 (b). Despite part (a), show that f is discontinuous at (0, 0). (c). Show that f is discontinuous on two enti

> Graph and discuss the continuity of the function sin xy if ху # 0 f(x, y) = ху 1 if xy = 0

> Match the function (a) with its graph (labeled A–F below) and (b) with its contour map (labeled I–VI). Give reasons for your choices. z = (1 - x2) (1 - y2) B D E II III IV VI yA (OKO C O O O O).O O O) O O KO C O

> Match the function (a) with its graph (labeled A–F below) and (b) with its contour map (labeled I–VI). Give reasons for your choices. z = sin x - sin y B D E II III IV VI yA (OKO C O O O O).O O O) O O KO C O OD

> Determine the set of points at which the function is continuous. ху if (x, y) # (0, 0) 2 f(x, y) = if (x, y) = (0, 0)

> Determine the set of points at which the function is continuous. x²y³ f(x, y) = { ² 2.x² + if (x, y) + (0, 0) 1 if (x, y) = (0, 0)

> Match the function (a) with its graph (labeled A–F below) and (b) with its contour map (labeled I–VI). Give reasons for your choices. z = sin(xy) B D E II III IV VI yA (OKO C O O O O).O O O) O O KO C O OD O

> Determine the set of points at which the function is continuous. f (x, y, z) = arcsin (x2 + y2 + z2)

> Find the velocity, acceleration, and speed of a particle with the given position function. Sketch the path of the particle and draw the velocity and acceleration vectors for the specified value of t. r(t) = et i + e2t j, t = 0

> Determine the set of points at which the function is continuous. G (x, y) = ln (1 + x – y)

> Determine the set of points at which the function is continuous. e* + e H(x, y) = eу — 1

> Use a computer to graph the function using various domains and viewpoints. Get a printout of one that, in your opinion, gives a good view. If your software also produces level curves, then plot some contour lines of the same function and compare with the

> Graph the function and observe where it is discontinuous. Then use the formula to explain what you have observed. 1 f(x, y) = 1 – x² – y? ,2

> Graph the function and observe where it is discontinuous. Then use the formula to explain what you have observed. f (x, y) = e1/(x-y)

> Sketch both a contour map and a graph of the function and compare them. f(x, y) = V36 – 9x² – 4y²

> Sketch both a contour map and a graph of the function and compare them. f (x, y) = x2 + 9y2

> Find h (x, y) = g (f (x, y)) and the set of points at which h is continuous. g(t) = t + In t, f(x, y) : 1 - ху 1+ x?y? .2,2

> Use a computer graph of the function to explain why the limit does not exist. хуз lim (x, y)(0, 0) x? + y6

> Find the limit, if it exists, or show that the limit does not exist. xy4 lim (x, y)- (0, 0) x + y® ,2 8

> The temperature-humidity index I (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write I = f (T, h). The following table of values of I is an excerpt from a table compile

> The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f (v, t) are recorded in feet in Table 4. Table 4: (a). What is the value of f (40,

> Two contour maps are shown. One is for a function f whose graph is a cone. The other is for a function t whose graph is a paraboloid. Which is which, and why?

> Level curves (isothermals) are shown for the typical water temperature (in 0C) in Long Lake (Minnesota) as a function of depth and time of year. Estimate the temperature in the lake on June 9 (day 160) at a depth of 10 m and on June 29 (day 180) at a dep

> Shown is a contour map of atmospheric pressure in North America on August 12, 2008. On the level curves (called isobars) the pressure is indicated in millibars (mb). (a). Estimate the pressure at C (Chicago), N (Nashville), S (San Francisco), and V (Va

> The position function of a spaceship is and the coordinates of a space station are (6, 4, 9). The captain wants the spaceship to coast into the space station. When should the engines be turned off? 4 r(t) = (3 + f)i + (2 + In f) j + (7- k t2 + 1,

> A contour map for a function f is shown. Use it to estimate the values of f (-3, 3) and f (3, -2). What can you say about the shape of the graph? 70 60 50 40 -1 30 20 10

> The magnitude of the acceleration vector a is 10 cm/s2. Use the figure to estimate the tangential and normal components of a. a

> Sketch the graph of the function. f (x, y) = x2

> The body mass index is defined in Exercise 39. Draw the level curve of this function corresponding to someone who is 200 cm tall and weighs 80 kg. Find the weights and heights of two other people with that same level curve. Exercise 39: The body mass i

> In Example 2 we considered the function W = f (T, v), where W is the wind-chill index, T is the actual temperature, and v is the wind speed. A numerical representation is given in Table 1 on page 889. Table: (a). What is the value of f (-15, 40)? What

> The body mass index (BMI) of a person is defined by where m is the person’s mass (in kilograms) and h is the height (in meters). Draw the level curves B (m, h) = 18.5, B (m, h) = 25, B (m, h) = 30, and B (m, h) = 40. A rough guideline i

> Find and sketch the domain of the function. f(x, y, 2) = /4 – x² + v9 – y² + VT –

> A manufacturer has modeled its yearly production function P (the monetary value of its entire production in millions of dollars) as a Cobb-Douglas function P (L, K) = 1.47L0.65K0.35 where L is the number of labor hours (in thousands) and K is the inves

> The wind-chill index W discussed in Example 2 has been modeled by the following function: Check to see how closely this model agrees with the values in Table 1 for a few values of T and v. W(T, v) 13.12 + 0.6215T – 11.37v0.16 + 0.3965TV0.16

> What is the connection between vector functions and space curves?