Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 1CYU:
Determine which of the following limits exist. Compute the limits that exist. limx6x24x12x6.Problem 2CYU:
Determine which of the following limits exist. Compute the limits that exist. limx64x+12x6Problem 1E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 2E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 3E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 4E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 5E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 6E:
For each of the following functions g(x), dtermine whether limx3g(x) exists. If so, give the limit.Problem 7E:
Determine which of the following limits exist. Compute the limits that exist. limx1(16x)Problem 9E:
Determine which of the following limits exist. Compute the limits that exist. limx3x2+16Problem 10E:
Determine which of the following limits exist. Compute the limits that exist. limx4(x37)Problem 11E:
Determine which of the following limits exist. Compute the limits that exist. limx5x2+15+xProblem 12E:
Determine which of the following limits exist. Compute the limits that exist. limx6(6x+3x1x)(x24)Problem 14E:
Determine which of the following limits exist. Compute the limits that exist. limx85x413x2+2Problem 15E:
Determine which of the following limits exist. Compute the limits that exist. limx5x25x3683xProblem 16E:
Determine which of the following limits exist. Compute the limits that exist. limx10(2x215x50)20Problem 17E:
Determine which of the following limits exist. Compute the limits that exist. limx0x2+3xxProblem 18E:
Determine which of the following limits exist. Compute the limits that exist. limx1x21x1Problem 19E:
Determine which of the following limits exist. Compute the limits that exist. limx22x2+4xx2Problem 20E:
Determine which of the following limits exist. Compute the limits that exist. limx3x2x6x3Problem 21E:
Determine which of the following limits exist. Compute the limits that exist. limx4x2164xProblem 22E:
Determine which of the following limits exist. Compute the limits that exist. limx52x10x225Problem 23E:
Determine which of the following limits exist. Compute the limits that exist. limx6x26xx25x6Problem 24E:
Determine which of the following limits exist. Compute the limits that exist. limx7x32x2+3xx2Problem 25E:
Determine which of the following limits exist. Compute the limits that exist. limx8x2+64x8Problem 27E:
Compute the limits that exist, given that limx0f(x)=12 and limx0g(x)=12 a. limx0(f(x)+g(x)) b....Problem 33E:
In Exercise 3336, apply the three- step method to compute f(x) for the given function. Follow the...Problem 34E:
In Exercises 33-36, apply the three step method to compute f(x) for given function. Follow the steps...Problem 35E:
In Exercises 33-36, apply the three step method to compute f(x) for given function. Follow the steps...Problem 36E:
In Exercises 33-36, apply the three step method to compute f(x) for given function. Follow the steps...Problem 37E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 38E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 39E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 40E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 41E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 48E:
In Exercises 37-48, use limits to compute f(x). [Hint: In Exercises 45-48 use the rationalization...Problem 50E:
Each limit in Exercises 49-54 is a definition of f(a). Determine the function f(x) and the value of...Problem 51E:
Each limit in Exercises 49-54 is a definition of f(a). Determine the function f(x) and the value of...Problem 52E:
Each limit in Exercises 49-54 is a definition of f(a). Determine the function f(x) and the value of...Problem 53E:
Each limit in Exercises 49-54 is a definition of f(a). Determine the function f(x) and the value of...Problem 54E:
Each limit in Exercises 49-54 is a definition of f(a). Determine the function f(x) and the value of...Problem 55E:
Compute the following limits. limx1x2Problem 56E:
Compute the following limits. limx1x2Problem 57E:
Compute the following limits. limx5x+33x2Problem 58E:
Compute the following limits. limx1x8Problem 59E:
Compute the following limits. limx10x+100x230Problem 60E:
Compute the following limits. limxx2+xx21Problem 67E:
Technology Exercises Examine the graph of the function and evaluate the function-at-large values of...Problem 68E:
Technology Exercises Examine the graph of the function and evaluate the function-at-large values of...Browse All Chapters of This Textbook
Chapter 0 - FunctionsChapter 0.1 - Functions And Their GraphsChapter 0.2 - Some Important FunctionsChapter 0.3 - The Algebra Of FunctionsChapter 0.4 - Zeros Of Functions—the Quadratic Formula And FactoringChapter 0.5 - Exponents And Power FunctionsChapter 0.6 - Functions And Graphs In ApplicationsChapter 1 - The DerivativeChapter 1.1 - The Slope Of A Straight LineChapter 1.2 - The Slope Of A Curve At A Point
Chapter 1.3 - The Derivative And LimitsChapter 1.4 - Limits And The DerivativeChapter 1.5 - Differentiability And ContinuityChapter 1.6 - Some Rules For DifferentiationChapter 1.7 - More About DerivativesChapter 1.8 - The Derivative As A Rate Of ChangeChapter 2 - Applications Of The DerivativeChapter 2.1 - Describing Graphs Of FunctionsChapter 2.2 - The First- And Second-derivative RulesChapter 2.3 - The First- And Second-derivative Tests And Curve SketchingChapter 2.4 - Curve Sketching (conclusion)Chapter 2.5 - Optimization ProblemsChapter 2.6 - Further Optimization ProblemsChapter 2.7 - Applications Of Derivatives To Business And EconomicsChapter 3 - Techniques Of DifferentiationChapter 3.1 - The Product And Quotient RulesChapter 3.2 - The Chain RuleChapter 3.3 - Implicit Differentiation And Related RatesChapter 4 - The Exponential And Natural Logarithm FunctionsChapter 4.1 - Exponential FunctionsChapter 4.2 - The Exponential Function ExChapter 4.3 - Differentiation Of Exponential FunctionsChapter 4.4 - The Natural Logarithm FunctionChapter 4.5 - The Derivative Of Ln XChapter 4.6 - Properties Of The Natural Logarithm FunctionChapter 5 - Applications Of The Exponential And Natural Logarithm FunctionsChapter 5.1 - Exponential Growth And DecayChapter 5.2 - Compound InterestChapter 5.3 - Applications Of The Natural Logarithm Function To EconomicsChapter 5.4 - Further Exponential ModelsChapter 6 - The Definite IntegralChapter 6.1 - AntidifferentiationChapter 6.2 - The Definite Integral And Net Change Of A FunctionChapter 6.3 - The Definite Integral And Area Under A GraphChapter 6.4 - Areas In The Xy-planeChapter 6.5 - Applications Of The Definite IntegralChapter 7 - Functions Of Several VariablesChapter 7.1 - Examples Of Functions Of Several VariablesChapter 7.2 - Partial DerivativesChapter 7.3 - Maxima And Minima Of Functions Of Several VariablesChapter 7.4 - Lagrange Multipliers And Constrained OptimizationChapter 7.5 - The Method Of Least SquaresChapter 7.6 - Double IntegralsChapter 8 - The Trigonometric FunctionsChapter 8.1 - Radian Measure Of AnglesChapter 8.2 - The Sine And The CosineChapter 8.3 - Differentiation And Integration Of Sin T And Cos TChapter 8.4 - The Tangent And Other Trigonometric FunctionsChapter 9 - Techniques Of IntegrationChapter 9.1 - Integration By SubstitutionChapter 9.2 - Integration By PartsChapter 9.3 - Evaluation Of Definite IntegralsChapter 9.4 - Approximation Of Definite IntegralsChapter 9.5 - Some Applications Of The IntegralChapter 9.6 - Improper IntegralsChapter 10 - Differential EquationsChapter 10.1 - Solutions Of Differential EquationsChapter 10.2 - Separation Of VariablesChapter 10.3 - First-order Linear Differential EquationsChapter 10.4 - Applications Of First-order Linear Differential EquationsChapter 10.5 - Graphing Solutions Of Differential EquationsChapter 10.6 - Applications Of Differential EquationsChapter 10.7 - Numerical Solution Of Differential EquationsChapter 11 - Taylor Polynomials And Infinite SeriesChapter 11.1 - Taylor PolynomialsChapter 11.2 - The Newton–raphson AlgorithmChapter 11.3 - Infinite SeriesChapter 11.4 - Series With Positive TermsChapter 11.5 - Taylor SeriesChapter 12 - Probability And CalculusChapter 12.1 - Discrete Random VariablesChapter 12.2 - Continuous Random VariablesChapter 12.3 - Expected Value And VarianceChapter 12.4 - Exponential And Normal Random VariablesChapter 12.5 - Poisson And Geometric Random Variables
Book Details
Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums. The strategic organization of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.
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