Calculus: Early Transcendentals (3rd Ed...3rd EditionWilliam L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz Publisher: PEARSONISBN: 9780134763644
Calculus: Early Transcendentals (3rd Ed...
Solutions for Calculus: Early Transcendentals (3rd Edition)
Problem 2QC:
Use Theorem 2.4 to compute limx15x43x2+8x6x+1.Problem 3QC:
Evaluate limx5x27x+10x5.Problem 4QC:
Suppose f satisfies 1f(x)1+x26 for all values of x near zero. Find limx0f(x), if possible.Problem 2E:
Evaluate limx1(x3+3x23x+1).Problem 4E:
Evaluate limx4(x44x13x1).Problem 6E:
Evaluate limx5(4x2100x5).Problem 7E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 8E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 9E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 10E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 11E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 12E:
Applying limit laws Assume limx1f(x)=8, limx1g(x)=3, and limx1h(x)=2. Compute the following limits...Problem 13E:
Assume limx1f(x)=8 limx1g(x)=3, and limx1h(x)=2. Compute the following limits and state the limit...Problem 27E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 31E:
Evaluating limits Evaluate the following limits, where c and k are constants. 61. limx2(5x6)3/2Problem 32E:
Evaluating limits Evaluate the following limits, where c and k are constants. 60. limh0100(10h1)11+2Problem 33E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 39. limx1x21x1Problem 34E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 40....Problem 35E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 41....Problem 36E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 42....Problem 37E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 43....Problem 38E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 44....Problem 39E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 45....Problem 40E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 46....Problem 41E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 47. limx9x3x9Problem 42E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 43E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 44E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 48....Problem 45E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 49....Problem 46E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 50....Problem 47E:
Other techniques Evaluate the following limits, where a and b are fixed real numbers. 51....Problem 48E:
Evaluating limits Evaluate the following limits, where c and k are constants. 66. limxcx22cx+c2xcProblem 49E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 50E:
Evaluating limits Evaluate the following limits, where c and k are constants. 62. limx31x2+2x115x3Problem 51E:
Evaluating limits Evaluate the following limits, where c and k are constants. 63. limx110x91x1Problem 52E:
Evaluating limits Evaluate the following limits, where c and k are constants. 64. limx2(1x22x22x)Problem 53E:
Evaluating limits Evaluate the following limits, where c and k are constants. 65. limh0(5+h)225hProblem 58E:
Limits involving conjugates Evaluate the following limits. 80. limx0xcx+11, where c is a nonzero...Problem 59E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 60E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 61E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 62E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 63E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 64E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 65E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 66E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 67E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 68E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 69E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 70E:
Evaluating limits Find the following limits or state that they do not exist. Assume a, b, c, and k...Problem 71E:
Explain why or why not Determine whether the following statements are true and give an explanation...Problem 72E:
One-sided limits Let g(x)={5x15ifx46x+1ifx4. Compute the following limits or state that they do not...Problem 73E:
One-sided limits Let f(x)={x2ifx1x+1ifx1. Compute the following limits or state that they do not...Problem 74E:
One-sided limits Let f(x)={0ifx525x2if5x53xifx5. Compute the following limits or state that they do...Problem 78E:
Torricellis Law A cylindrical tank is filled with water to a depth of 9 meters. At t = 0, a drain in...Problem 79E:
Limit of the radius of a cylinder A right circular cylinder with a height of 10 cm and a surface...Problem 80E:
A problem from relativity theory Suppose a spaceship of length L0 travels at a high speed v relative...Problem 81E:
Applying the Squeeze Theorem a. Show that xxsin1xx, for x 0. b. Illustrate the inequalities in part...Problem 82E:
A cosine limit by the Squeeze Theorem It can be shown that 1x22cosx1, for x near 0. a. Illustrate...Problem 83E:
A sine limit by the Squeeze Theorem It can be shown that 1x26sinx1, for x near 0. a. Illustrate...Problem 84E:
A logarithm limit by the Squeeze Theorem a. Draw a graph to verify that |x| x2 ln x2 |x|, for l x...Problem 85E:
Absolute value limit Show that limx0x=0 by first evaluating limx0x and limx0+x. Recall that...Problem 86E:
Absolute value limit Show that limxax=a, for any real number. (Hint: Consider the cases a 0 and a ...Problem 87E:
Finding a constant Suppose f(x)={x25x+6x3ifx3aifx=3. Determine a value of the constant a for which...Problem 88E:
Finding a constant Suppose f(x)={3x+bifx2x2ifx2. Determine a value of the constant b for which...Problem 89E:
Finding a constant Suppose g(x)={x25xifx1ax37ifx1. Determine a value of the constant a for which...Problem 90E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 91E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 92E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 93E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 94E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 95E:
Slope of a tangent line a. Sketch a graph of y = 2x and carefully draw three secant lines connecting...Problem 97E:
Even function limits Suppose f is an even function where limx1f(x)=5 and limx1+f(x)=6. Find...Problem 98E:
Odd function limits Suppose g is an even function where limx1g(x)=5 and limx1+g(x)=6. Find limx1g(x)...Problem 99E:
Useful factorization formula Calculate the following limits using the factorization formula...Problem 100E:
Evaluate limx16x42x16.Problem 101E:
Creating functions satisfying given limit conditions Find functions f and g such that limx1f(x)=0...Problem 102E:
Creating functions satisfying given limit conditions Find a function f satisfying limx1(f(x)x1)=2.Problem 103E:
Finding constants Find constants b and c in the polynomial p(x) = x2 + bx + c such that...Browse All Chapters of This Textbook
Chapter 1 - FunctionsChapter 1.1 - Review Of FunctionsChapter 1.2 - Representing FunctionsChapter 1.3 - Inverse, Exponential, And Logarithmic FunctionsChapter 1.4 - Trigonometric Functions And Their InversesChapter 2 - LimitsChapter 2.1 - The Idea Of LimitsChapter 2.2 - Definitions Of LimitsChapter 2.3 - Techniques For Computing LimitsChapter 2.4 - Infinite Limits
Chapter 2.5 - Limits At InfinityChapter 2.6 - ContinuityChapter 2.7 - Precise Definitions Of LimitsChapter 3 - DerivativesChapter 3.1 - Introducing The DerivativesChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Rules Of DifferentiationChapter 3.4 - The Product And Quotient RulesChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - Derivatives As A Rates Of ChangeChapter 3.7 - The Chain RuleChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Logarithmic And Exponential FunctionsChapter 3.10 - Derivatives Of Inverse Trigonometric FunctionsChapter 3.11 - Related RatesChapter 4 - Applications Of The DerivativeChapter 4.1 - Maxima And MinimaChapter 4.2 - Mean Value TheoremChapter 4.3 - What Derivative Tell UsChapter 4.4 - Graphing FunctionsChapter 4.5 - Optimization ProblemsChapter 4.6 - Linear Approximation And DifferentialsChapter 4.7 - L'hopital's RuleChapter 4.8 - Newton's MethodChapter 4.9 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating Areas Under CurvesChapter 5.2 - Definite IntegralsChapter 5.3 - Fundamental Theorem Of CalculusChapter 5.4 - Working With IntegralsChapter 5.5 - Substitution RuleChapter 6 - Applications Of IntegrationChapter 6.1 - Velocity And Net ChangeChapter 6.2 - Regions Between CurvesChapter 6.3 - Volume By SlicingChapter 6.4 - Volume By ShellsChapter 6.5 - Length Of CurvesChapter 6.6 - Surface AreaChapter 6.7 - Physical ApplicationsChapter 7 - Logarithmic And Exponential, And Hyperbolic FunctionsChapter 7.1 - Logarithmic And Exponential Functions RevisitedChapter 7.2 - Exponential ModelsChapter 7.3 - Hyperbolic FunctionsChapter 8 - Integration TechniquesChapter 8.1 - Basic ApproachesChapter 8.2 - Integration By PartsChapter 8.3 - Trigonometric IntegralsChapter 8.4 - Trigonometric SubstitutionsChapter 8.5 - Partial FractionsChapter 8.6 - Integration StrategiesChapter 8.7 - Other Methods Of IntegrationChapter 8.8 - Numerical IntegrationChapter 8.9 - Improper IntegralsChapter 9 - Differential EquationsChapter 9.1 - Basic IdeasChapter 9.2 - Direction Fields And Euler's MethodChapter 9.3 - Separable Differential EquationsChapter 9.4 - Special First-order Linear Differential EquationsChapter 9.5 - Modeling With Differential EquationsChapter 10 - Sequences And Infinite SeriesChapter 10.1 - An OverviewChapter 10.2 - SequencesChapter 10.3 - Infinite SeriesChapter 10.4 - The Divergence And Integral TestsChapter 10.5 - Comparison TestsChapter 10.6 - Alternating SeriesChapter 10.7 - The Ration And Root TestsChapter 10.8 - Choosing A Convergence TestChapter 11 - Power SeriesChapter 11.1 - Approximating Functions With PolynomialsChapter 11.2 - Properties Of Power SeriesChapter 11.3 - Taylor SeriesChapter 11.4 - Working With Taylor SeriesChapter 12 - Parametric And Polar CurvesChapter 12.1 - Parametric EquationsChapter 12.2 - Polar CoordinatesChapter 12.3 - Calculus In Polar CoordinatesChapter 12.4 - Conic SectionsChapter 13 - Vectors And The Geometry Of SpaceChapter 13.1 - Vectors In The PlaneChapter 13.2 - Vectors In Three DimensionsChapter 13.3 - Dot ProductsChapter 13.4 - Cross ProductsChapter 13.5 - Lines And Planes In SpaceChapter 13.6 - Cylinders And Quadric SurfacesChapter 14 - Vector-valued FunctionsChapter 14.1 - Vector-valued FunctionsChapter 14.2 - Calculus Of Vector-valued FunctionsChapter 14.3 - Motion In SpaceChapter 14.4 - Length Of CurvesChapter 14.5 - Curvature And Normal VectorsChapter 15 - Functions Of Several VariablesChapter 15.1 - Graphs And Level CurvesChapter 15.2 - Limits And ContinuityChapter 15.3 - Partial DerivativesChapter 15.4 - The Chain RuleChapter 15.5 - Directional Derivatives And The GradientChapter 15.6 - Tangent Planes And Linear ProblemsChapter 15.7 - Maximum/minimum ProblemsChapter 15.8 - Lagrange MultipliersChapter 16 - Multiple IntegrationChapter 16.1 - Double Integrals Over Rectangular RegionsChapter 16.2 - Double Integrals Over General RegionsChapter 16.3 - Double Integrals In Polar CoordinatesChapter 16.4 - Triple IntegralsChapter 16.5 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 16.6 - Integrals For Mass CalculationsChapter 16.7 - Change Of Variables In Multiple IntegralsChapter 17 - Vector CalculusChapter 17.1 - Vector FieldsChapter 17.2 - Line IntegralsChapter 17.3 - Conservative Vector FieldsChapter 17.4 - Green's TheoremChapter 17.5 - Divergence And CurlChapter 17.6 - Surface IntegralsChapter 17.7 - Stokes' TheoremChapter 17.8 - Divergence TheoremChapter B - Algebra ReviewChapter C - Complex Numbers
Sample Solutions for this Textbook
We offer sample solutions for Calculus: Early Transcendentals (3rd Edition) homework problems. See examples below:
Chapter 1, Problem 1REChapter 2, Problem 1REChapter 3, Problem 1REChapter 4, Problem 1REChapter 5, Problem 1REChapter 6, Problem 1REChapter 7, Problem 1REChapter 8, Problem 1REChapter 9, Problem 1RE
Chapter 10, Problem 1REChapter 11, Problem 1REChapter 12, Problem 1REChapter 13, Problem 1REThe given vector valued function is r(t)=〈cost,et,t〉+C. Substitute t=0 in the vector as follows....The given function is, g(x,y)=ex+y. Let ex+y=k. Take log on both sides. ex+y=kln(ex+y)=ln(k)x+y=lnk...Chapter 16, Problem 1REChapter 17, Problem 1REChapter B, Problem 1EChapter C, Problem 1E
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