CALCULUS, VOLUME 1 (OER)17th EditionOpenStax Publisher: XANEDU CISBN: 2810022307715
CALCULUS, VOLUME 1 (OER)
Solutions for CALCULUS,VOLUME 1 (OER)
Problem 377E:
[T] Find expressions for coshx+sinhx and coshxsinhx . Use a calculator to graph these functions and...Problem 379E:
Show that cosh(x) and sinh(x) satisfy y=y .Problem 380E:
Use the quotient rule to verify that tanh(x)=sech2(x) .Problem 381E:
Derive cosh2(x)+sinh2(x)=cosh(2x) from the definition.Problem 383E:
Prove sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y) by changing the expression to exponentials.Problem 385E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 386E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 387E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 388E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 389E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 390E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 391E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 392E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 393E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 394E:
For the following exercises, find the derivatives of the given functions and graph along with the...Problem 395E:
For the following exercises, find the antiderivatives for the given functions. 395. cosh(2x+1)Problem 396E:
For the following exercises, find the antiderivatives for the given functions. 396. tanh(3x+2)Problem 397E:
For the following exercises, find the antiderivatives for the given functions. 397. xcosh(x2)Problem 398E:
For the following exercises, find the antiderivatives for the given functions. 398. 3x3tanh(x4)Problem 399E:
For the following exercises, find the antiderivatives for the given functions. 399. cosh2(x)sinh(x)Problem 400E:
For the following exercises, find the antiderivatives for the given functions. 400. tan2(x)sech2(x)Problem 401E:
For the following exercises, find the antiderivatives for the given functions. 401. sinh(x)1+cosh(x)Problem 402E:
For the following exercises, find the antiderivatives for the given functions. 402. coth(x)Problem 403E:
For the following exercises, find the antiderivatives for the given functions. 403. cosh(x)+sinh(x)Problem 404E:
For the following exercises, find the antiderivatives for the given functions. 404....Problem 407E:
For the following exercises, find the derivatives for the functions. 407. sinh1(cosh(x))Problem 409E:
For the following exercises, find the derivatives for the functions. 409. tanh1(cos(x))Problem 411E:
For the following exercises, find the derivatives for the functions. 411. In(tanh1(x))Problem 413E:
For the following exercises, find the antiderivatives for the functions. 413. dx a 2 x 2Problem 414E:
For the following exercises, find the antiderivatives for the functions. 414. dx x 2 1 .Problem 415E:
For the following exercises, find the antiderivatives for the functions. 415. xdx x 2 1Problem 416E:
For the following exercises., find the antiderivatives for the functions. 416. dxx 1 x 2Problem 417E:
For the following exercises., find the antiderivatives for the functions. 417. e x e 2x 1Problem 419E:
For the following exercises, use the fact that a falling body with friction equal to velocity...Problem 420E:
For the following exercises, use the fact that a falling body with friction equal to velocity...Problem 421E:
For the following exercises, use the fact that a falling body with friction equal to velocity...Problem 422E:
For the following exercises, use this scenario: A cable hanging under its own weight has a slope...Problem 423E:
For the following exercises, use this scenario: A cable hanging under its own weight has a slope...Problem 424E:
For the following exercises, use this scenario: A cable hanging under its own weight has a slope...Problem 425E:
For the following exercises, solve each problem. 425. [T] A chain hangs from two posts 2 m apart to...Problem 426E:
For the following exercises, solve each problem. 426. [T] A chain hangs from two posts four meters...Problem 427E:
For the following exercises, solve each problem. 427. [T] A high-voltage power line is a catenary...Problem 428E:
For the following exercises, solve each problem. 428. A telephone line is a catenary described by...Problem 429E:
For the following exercises, solve each problem. 429. Prove the formula for the derivative of...Problem 430E:
For the following exercises, solve each problem. 430. Prove the formula for the derivative of...Problem 431E:
For the following exercises, solve each problem. 431. Prove the formula for the derivative of...Problem 432E:
Prove that (cosh(x)+sinh(x)n)=cosh(nx)+sinh(nx) .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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