Solutions for CALCULUS,VOLUME 1 (OER)
Problem 1SP:
Consider the graph in Figure 1.42 of the function y=sinx+cosx . Describe its overall shape. Is it...Problem 2SP:
Now consider other graphs of the form y=Asinx+Bcosx for various values of A and B. Sketch the graph...Problem 5SP:
5. Try to figure out the formula for the y-values.Problem 6SP:
6. The formula for the x-values is a little harder. The most helpful points from the table are...Problem 7SP:
7. If you found formulas for parts (5) and (6), show that they work together. That is, substitute...Problem 183E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 184E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 185E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 186E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 187E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 188E:
For the following exercises, use the horizontal line test to determine whether each of the given...Problem 189E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 190E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 191E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 192E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 193E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 194E:
For the following exercises, a. find the inverse function, and b. find the domain and range of the...Problem 195E:
For the following exercises, use the graph of f sketch the graph of its inverse function. 195.Problem 196E:
For the following exercises, use the graph of f sketch the graph of its inverse function. 196.Problem 197E:
For the following exercises, use the graph of f sketch the graph of its inverse function. 197.Problem 198E:
For the following exercises, use the graph of f to sketch the graph of its inverse function. 198.Problem 199E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 200E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 201E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 202E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 203E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 204E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 205E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 206E:
For the following exercises, use composition to determine which pairs of functions are inverses....Problem 207E:
For the following exercises, evaluate the functions. Give the exact value. 207. tan1(33)Problem 208E:
For the following exercises, evaluate the functions. Give the exact value. 208. cos1(22)Problem 209E:
For the following exercises, evaluate the functions. Give the exact value. 209. cot1(1)Problem 210E:
For the following exercises, evaluate the functions. Give the exact value. 210. sin1(1)Problem 211E:
For the following exercises, evaluate the functions. Give the exact value. 211. cos1(32)Problem 212E:
For the following exercises, evaluate the functions. Give the exact value. 212. cos(tan1(3))Problem 213E:
For the following exercises, evaluate the functions. Give the exact value. 213. sin(cos1( 2 2))Problem 214E:
For the following exercises, evaluate the functions. Give the exact value. 214. sin1(sin(3))Problem 215E:
For the following exercises, evaluate the functions. Give the exact value. 215. tan1(tan(6))Problem 216E:
The function C=T(F)=(5/9)(F32) converts degrees Fahrenheit to degrees Celsius. Find the inverse...Problem 217E:
[T] The velocity V (in centimeters per second) of blood in an artery at a distance x cm from the...Problem 218E:
A function that converts dress sizes in the United States to those in Europe is given by D(x)=2x+24...Problem 219E:
[T] The cost to remove a toxin from a lake is modeled by the function C(p)=75p/(85p) , where C is...Problem 220E:
[T] A race car is accelerating at a velocity given by v(t)=254t+54 , where v is the velocity (in...Problem 221E:
[T] An airplane’s Mach number M is the ratio of its speed to the speed of sound. When a plane is...Problem 222E:
[T] Using =2sin1(1M) , find the Mach number M for the following angles. a.=6b.=27c.=38Problem 223E:
[T] The temperature (in degrees Celsius) of a city in the northern United States can be modeled by...Problem 224E:
[T] The depth (in feet) of water at a dock changes with the rise and fall of tides. It is modeled by...Problem 225E:
[T] All object moving in simple harmonic motion is modeled by the function s(t)=6cos(t2) , where s...Problem 226E:
A local art gallery has a portrait 3 ft in height that is hung 2.5 ft above the eye level of an...Browse All Chapters of This Textbook
Chapter 1 - Functions And GraphsChapter 1.1 - Review Of FunctionsChapter 1.2 - Basic Classes Of FunctionsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Inverse FunctionsChapter 1.5 - Exponential And Logarithmic FunctionsChapter 2 - LimitsChapter 2.1 - A Preview Of CalculusChapter 2.2 - The Limit Of A FunctionChapter 2.3 - The Limit Laws
Chapter 2.4 - ContinuityChapter 2.5 - The Precise Definition Of A LimitChapter 3 - DerivativesChapter 3.1 - Defining The DerivativeChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - Derivatives As Rates Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Derivatives Of Inverse FunctionsChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Exponential And Logarithmic FunctionsChapter 4 - Applications Of DerivativesChapter 4.1 - Related RatesChapter 4.2 - Linear Approximations And DifferentialsChapter 4.3 - Maxima And MinimaChapter 4.4 - The Mean Value TheoremChapter 4.5 - Derivatives And The Shape Of A GraphChapter 4.6 - Limits At Infinity And AsymptotesChapter 4.7 - Applied Optimization ProblemsChapter 4.8 - L'hopitars RuleChapter 4.9 - Newton's MethodChapter 4.10 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating AreasChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Integration Formulas And The Net Change TheoremChapter 5.5 - SubstitutionChapter 5.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 5.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - Determining Volumes By SlicingChapter 6.3 - Volumes Of Revolution: Cylindrical ShellsChapter 6.4 - Arc Length Of A Curve And Surface AreaChapter 6.5 - Physical ApplicationsChapter 6.6 - Moments And Centers Of MassChapter 6.7 - Integrals, Exponential Functions, And LogarithmsChapter 6.8 - Exponential Growth And DecayChapter 6.9 - Calculus Of The Hyperbolic Functions
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