Student Solutions Manual for Calculus &...14th EditionLarry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar Publisher: PEARSONISBN: 9780134463230
Student Solutions Manual for Calculus &...
Solutions for Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version
Problem 2CYU:
Let f(x)=1/x4. a. Find its derivative. b. Find f(2).Problem 1E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 2E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 3E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 4E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 5E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 6E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 7E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 8E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 9E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 10E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 11E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 12E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 13E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 14E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 15E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 16E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 17E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x3 at x=12.Problem 18E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x5 at x=32.Problem 19E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=1x at x=23.Problem 20E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=13 at x=2.Problem 21E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x+11 at x=0.Problem 22E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x1/3 at x=8.Problem 23E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x at x=116.Problem 24E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=1x25 at x=32.Problem 25E:
Find the slope of the curve y=x4 at x=2.Problem 26E:
Find the slope of the curve y=x5 at x=13.Problem 27E:
If f(x)=x3, compute f(5) and f(5).Problem 28E:
If f(x)=2x+6, compute f(0) and f(0).Problem 29E:
If f(x)=x1/3, compute f(8) and f(8).Problem 30E:
If f(x)=1/x2, compute f(1) and f(1).Problem 31E:
If f(x)=1/x5, compute f(2) and f(2).Problem 32E:
If f(x)=x3/2, compute f(16) and f(16).Problem 33E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 34E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 35E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 36E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 37E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 38E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 39E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 40E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 41E:
The point-slope form of the equation of the tangent line to the graph of y=x4 at point (1,1) is...Problem 42E:
The tangent line to the graph of y=1x at the point P=(a,1a), where a0, is perpendicular to the line...Problem 43E:
The line y=2x+b is tangent to the graph y=x at the point P=(a,a). Find P and determine b.Problem 45E:
a. Find the point on the curve y=x where the tangent line is parallel to the line y=x8. b. On the...Problem 46E:
There are two points on the graph of y=x3 where the tangent lines are parallel to y=x. Find these...Problem 47E:
Is there any point on the graph of y=x3 where the tangent line is perpendicular to y=x? Justify your...Problem 48E:
The graph of y=f(x) goes through the point (2, 3) and the equation of the tangent line at that point...Problem 59E:
In Fig.15, the straight line y=14x+b is tangent to the graph of f(x)=x. Find the values of a and b....Problem 60E:
In Fig.16, the straight line is tangent to the graph of f(x)=1x. Find the value of a. Figure 16Problem 65E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 66E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 67E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 68E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 69E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 70E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 71E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 72E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 73E:
In Exercises 71-76, apply the threestep method to compute the derivative of the given function....Problem 74E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 75E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 76E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 77E:
Draw two graphs of your choice that represent a function y=f(x) and its vertical shift y=f(x)+3 Pick...Problem 78E:
Use the approach of Exercise 77 to show that ddxf(x)=ddx(f(x)+c) For any costant c.[Hint: Compare...Problem 81E:
Technology Exercises In Exercises 79-84, use a derivative routine to obtain the value of the...Problem 82E:
Technology Exercises In Exercises 79-84, use a derivative routine to obtain the value of the...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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