Single Variable Calculus, 8th Edition Test Bank

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Stewart - Calculus 8e Chapter 1 Form A1.Find the domain of the function.2.Determine whetherfis even, odd, or neither.3.The graphs ofandare given.a) For what values ofis?b) Find the values ofand.4.It makes sense that the larger the area of a region, the larger the number of species that inhabit theregion. Many ecologists have modeled the species-area relation with a power function and, inparticular, the number of speciesSof bats living in caves in central Mexico has been related to thesurface areaAmeasured inof the caves by the equation(a) The cave called mission impossible near puebla, mexico, has suface area of.How many species of bats would expect to find in that cave?(b) If you discover thatspecies of bats live in cave estimate the area of the cave.

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Stewart - Calculus 8e Chapter 1 Form A5.Express the function in the form of.6.The position of a car is given by the values in the following table.Estimate the instantaneous velocity whenby averaging the velocities for the periods.7.Consider the following function.Determine the values ofafor whichexists.8.Find the limit.9.Evaluate the limit.10.Find the limit.

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Stewart - Calculus 8e Chapter 1 Form A11.Evaluate the limit.12.Evaluate the limit.13.Evaluate the limit.14.Find a numbersuch that if, then, where.15.Find the point at which the given function is discontinuous.16.Write an equation that expresses the fact that a functionfis continuous at the number.17.Find a functiongthat agrees withfforand is continuous on.18.Letand.Find.19.Find the limit.20.Find the numbers, if any, where the functionis discontinuous.

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Stewart - Calculus 8e Chapter 1 Form AAnswer Key1.2.even3.a) –2, 10b),4.a)speciesb)5.6.ft/s7.8.9.10.011.12.13.14.

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Stewart - Calculus 8e Chapter 1 Form A16.17.18.–619.20.

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Stewart - Calculus 8e Chapter 1 Form B1.Find the domain of the function.2.A spherical balloon with radiusinches has volume.Find a function that represents the amount of air required to inflate the balloon from a radius ofinches to a radius ofinches.3.It makes sense that the larger the area of a region, the larger the number of species that inhabit theregion. Many ecologists have modeled the species-area relation with a power function and, inparticular, the number of speciesSof bats living in caves in central Mexico has been related to thesurface areaAmeasured inof the caves by the equation(a) The cave called mission impossible near puebla, mexico, has suface area of.How many species of bats would expect to find in that cave?(b) If you discover thatspecies of bats live in cave estimate the area of the cave.4.A spherical balloon with radiusinches has volume.Find a function that represents the amount of air required to inflate the balloon from a radius ofinches to a radius ofinches.5.A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s.Express the radiusrof this circle as a function of the timet(in seconds) and findifAis thearea of this circle as a function of the radius.6.The position of a car is given by the values in the following table.Estimate the instantaneous velocity whenby averaging the velocities for the periods.

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Stewart - Calculus 8e Chapter 1 Form B7.Evaluate the functionat the given numbers (correct to six decimal places). Use the results to guess the value of the limit8.By graphing the functionand zooming in toward the point where the graph crosses they-axis, estimate the value of

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Stewart - Calculus 8e Chapter 1 Form B9.Consider the following function.Determine the values ofafor whichexists.10.How close to 2 do we have to takexso thatis within a distance of 0.01 from 13?11.Find the limit.12.Evaluate the limit.13.Find the limit.14.Evaluate the limit.15.Find the limit if.16.Use a graph to find a numbersuch thatwhenever.

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Stewart - Calculus 8e Chapter 1 Form B17.Iffandgare continuous functions with18.The following figure shows a portion of the graph of a functionfdefined on the interval.Sketch the complete graph offif it is knownfis odd.1–1x1–1y19.Letand.Find.20.Find the limit, if it exists.

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Stewart - Calculus 8e Chapter 1 Form BAnswer Key1.2.3.a)speciesb)4.125.6.ft/s7.8.9.10.11.12.10713.014.15.16.17.

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Stewart - Calculus 8e Chapter 1 Form B18.1–1x1–1y19.–620.

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Stewart - Calculus 8e Chapter 1 Form CSelect the correct answer for each question.____1.If, evaluate the difference quotient.a.b.c.d.he.none of these____2.Find the domain of the functiona.b.c.d.

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Stewart - Calculus 8e Chapter 1 Form C____3.The graph of the functionis given. State the value of.a.b.c.d.e.____4.Scientists have discovered that a linear relationship exists between the amount of flobberwormmucus secretions and the air temperature. When the temperature is 65°F, the flobberworms eachsecrete 16 grams of mucus a day; when the temperature is 95°F, they each secrete 22 grams ofmucus a day.Find a functionM(t) that gives the amount of mucus secreted on a given day, wheretis the temperature of that day in degrees Fahrenheit.a.b.c.d.

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Stewart - Calculus 8e Chapter 1 Form C____5.Graph the function by hand, not by plotting points, but by starting with the graph of one of thestandard functions and then applying the appropriate transformations.a.12345–1–2–3–4–5x12345–1–2–3–4–5yc.12345–1–2–3–4–5x12345–1–2–3–4–5yb.12345–1–2–3–4–5x12345–1–2–3–4–5yd.12345–1–2–3–4–5x12345–1–2–3–4–5y

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Stewart - Calculus 8e Chapter 1 Form C____6.Sketch the graph ofover one period.a.12345678–1–2x12345–1–2–3–4–5yc.12345678–1–2x12345–1–2–3–4–5yb.12345678–1–2x12345–1–2–3–4–5yd.12345678–1–2x12345–1–2–3–4–5y

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Stewart - Calculus 8e Chapter 1 Form C____7.The graph of the functionhas been stretched horizontally by a factor of 2.Find the function for the transformed graph.a.b.c.d.____8.A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles thenumber of heartbeats aftertminutes. When the data in the table are graphed, the slope of thetangent line represents the heart rate in beats per minute. The monitor estimates this value bycalculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42minutes using the secant line between the points with.a.b.c.d.e.f.____9.If a ball is thrown into the air with a velocity of, its height (in feet) aftertseconds is givenby.Find the velocity whena.ft/sb.ft/sc.ft/sd.ft/s

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Stewart - Calculus 8e Chapter 1 Form C____10.The position of a car is given by the values in the following table.(seconds)01234(meters)021.925.869.292.2Find the average velocity for the time period beginning whenand lasting 2 seconds.a.ft/sb.ft/sc.33.5 ft/sd.ft/se.33.2 ft/s____11.Suppose the distances(in feet) covered by a car moving along a straight road aftertsec is givenby the functionCalculate the (instantaneous) velocity of the car whena.223 ft/secb.16 ft/secc.560 ft/secd.4130 ft/sec

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Stewart - Calculus 8e Chapter 1 Form C____12.Sketch the graph of the functionfand evaluatea.12345–1–2–3–4–5x12345–1–2–3–4–5yDoes not existc.12345–1–2–3–4–5x12345–1–2–3–4–5yDoes not existb.12345–1–2–3–4–5x12345–1–2–3–4–5y2d.12345–1–2–3–4–5x12345–1–2–3–4–5y5

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Stewart - Calculus 8e Chapter 1 Form C____13.Evaluate the limit.a.b.c.d.e.____14.Iffinda.b.c.0d.e.____15.Find the limit.a.b.c.d.e.

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Stewart - Calculus 8e Chapter 1 Form C____16.Use the graph ofto guess at the limit, if it exists.12345–1–2–3–4–5x12345–1–2–3–4–5ya.–2b.–1c.Does not existd.–3____17.Let. Find the following limits.a.b.c.d.e.

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Stewart - Calculus 8e Chapter 1 Form C____18.Which of the given functions is discontinuous?a.b.____19.Find the numbers, if any, where the functionis discontinuous.a.b.2c.1d.0____20.Find the interval(s) whereis continuous.a.b.c.d.

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Stewart - Calculus 8e Chapter 1 Form CAnswer Key1.E2.A3.C4.D5.C6.C7.C8.F9.B10.E11.A12.D13.D14.B15.A16.C17.D18.A19.C20.C

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Stewart - Calculus 8e Chapter 1 Form CSelect the correct answer for each question.____1.Which of the following graphs is neither even nor odd?a.b.c.____2.Find the domain of the function.a.(–b.c.d.(–____3.The graph shown gives the weight of a certain person as a function of age. Find the age at whichthe person started an exercise program.a.20b.54c.38d.e.35

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Stewart - Calculus 8e Chapter 1 Form C____4.The relationship between the Fahrenheit and Celsius temperature scales is given by the linearfunction.What is theF-intercept and what does it represent?a., Fahrenheit temperature corresponding tob., Celsius temperature corresponding toc.32, Celsius temperature corresponding tod.0, Fahrenheit temperature corresponding toe.32, Fahrenheit temperature corresponding to____5.Use the table to evaluate the expression.123456321012652346a.5b.2c.3d.4e.6

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Stewart - Calculus 8e Chapter 1 Form C____6.Find the functionand its domain ifand.a.b.c.d.____7.The displacement (in feet) of a certain particle moving in a straight line is given bywheretis measured in seconds. Find the average velocity over the intervalRound your answer to three decimal places.a.b.c.d.e.f.

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Stewart - Calculus 8e Chapter 1 Form C____8.If a rock is thrown upward on the planet Mars with a velocity of, its height in meterstseconds later is given by.Find the average velocity over the time interval.a.m/sb.m/sc.m/sd.m/se.m/s____9.The pointlies on the curve. If is the pointQ, use your calculator tofind the slope of the secant linePQ(correct to six decimal places) for the valuea.b.c.d.e.____10.Find the value of..a.b.c.d.e.

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Stewart - Calculus 8e Chapter 1 Form C____11.Iffor allx,find.a.b.c.d.e.does not exist____12.Find the limit.a.b.c.0d.e.

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Stewart - Calculus 8e Chapter 1 Form C____13.Sketch the graph of the functionfand evaluatea.12345–1–2–3–4–5x12345–1–2–3–4–5y3c.12345–1–2–3–4–5x12345–1–2–3–4–5y3b.12345–1–2–3–4–5x12345–1–2–3–4–5y–1d.12345–1–2–3–4–5x12345–1–2–3–4–5y–1

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Stewart - Calculus 8e Chapter 1 Form C____14.Find the limit.a.0b.c.d.e.does not exist____15.Iffandgare continuous functions witha.b.c.d.e.____16.LetFind the value ofkthat will makefcontinuous ona.5b.46c.–4d.3

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Stewart - Calculus 8e Chapter 1 Form C____17.Suppose that the graph of is givenfis given. Describe how the graph of the functioncan be obtained from the graph off.a.Shift the graph 5 units to the left and 5 units down.b.Shift the graph 5 units to the left and 5 units up.c.Shift the graph 5 units to the right and 5 units up.d.Shift the graph 5 units to the right and 5 units down.e.None of these____18.The position of a car is given by the values in the following table.(seconds)01234(meters)021.925.869.292.2Find the average velocity for the time period beginning whenand lasting 2 seconds.a.ft/sb.ft/sc.33.5 ft/sd.ft/se.33.2 ft/s____19.Let. Find the following limits.a.b.c.d.e.

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