Domanda del libro di testo
Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.
f. sinh (2 ln 3)
84
views
Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testo
Briggs 3rd EditionCh. 7 - Logarithmic, Exponential Functions, and Hyperbolic FunctionsProblema 7.3.79d
Briggs 3rd EditionCh. 7 - Logarithmic, Exponential Functions, and Hyperbolic FunctionsProblema 7.3.79dCapitolo 7, Problema 7.3.79d
Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.
d. sech (sinh 0)
Guida verificata passo dopo passo1
Recall the definitions of the hyperbolic functions involved: \( \sinh x = \frac{e^{x} - e^{-x}}{2} \) and \( \sech x = \frac{1}{\cosh x} \), where \( \cosh x = \frac{e^{x} + e^{-x}}{2} \).
First, evaluate \( \sinh 0 \) by substituting \( x = 0 \) into the definition: \( \sinh 0 = \frac{e^{0} - e^{0}}{2} \).
Simplify the expression for \( \sinh 0 \) to find its exact value.
Next, substitute the value of \( \sinh 0 \) into the expression \( \sech(\sinh 0) \), which becomes \( \sech(\text{value}) = \frac{1}{\cosh(\text{value})} \).
Finally, evaluate \( \cosh(\text{value}) \) using its definition and simplify to find \( \sech(\sinh 0) \).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Hyperbolic Sine Function (sinh)
The hyperbolic sine function, sinh(x), is defined as (e^x - e^(-x))/2. It is an odd function and maps real numbers to real numbers. Evaluating sinh at zero gives sinh(0) = 0, which is a key step in simplifying expressions involving hyperbolic functions.
Video consigliato:
Percorso guidato
5:53
Graph of Sine and Cosine Function
Hyperbolic Secant Function (sech)
The hyperbolic secant function, sech(x), is defined as 1/cosh(x), where cosh(x) = (e^x + e^(-x))/2. It is always positive for real x and is used to find the reciprocal of the hyperbolic cosine. Understanding sech helps in evaluating expressions like sech(sinh 0).
Video consigliato:
Percorso guidato
6:22Graphs of Secant and Cosecant Functions
Function Composition and Simplification
Function composition involves applying one function to the result of another, such as sech(sinh 0). Simplifying requires evaluating the inner function first, then applying the outer function. This stepwise approach is essential for correctly simplifying nested hyperbolic expressions.
Video consigliato:
3:48Evaluate Composite Functions - Special Cases
Pratica correlata
Domanda del libro di testo
Chemotherapy In an experimental study at Dartmouth College, mice with tumors were treated with the chemotherapeutic drug Cisplatin. Before treatment, the tumors consisted entirely of clonogenic cells that divide rapidly, causing the tumors to double in size every 2.9 days. Immediately after treatment, 99% of the cells in the tumor became quiescent cells which do not divide and lose 50% of their volume every 5.7 days. For a particular mouse, assume the tumor size is 0.5 cm³ at the time of treatment.
d. Plot a graph of V(t) for 0 ≤ t ≤ 15. What happens to the size of the tumor, assuming there are no follow-up treatments with Cisplatin?
40
views
Domanda del libro di testo
Evaluating hyperbolic functions Use a calculator to evaluate each expression or state that the value does not exist. Report answers accurate to four decimal places to the right of the decimal point.
f. tan⁻¹(sinh x) |₋₃³
59
views
Domanda del libro di testo
Terminal velocity Refer to Exercises 95 and 96.
d. How tall must a cliff be so that the BASE jumper (m = 75 kg and k = 0.2) reaches 95% of terminal velocity? Assume the jumper needs at least 300 m at the end of free fall to deploy the chute and land safely.
70
views
Domanda del libro di testo
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.
e. The area under the curve y = 1/x and the x-axis on the interval [1, e] is 1.
51
views
Domanda del libro di testo
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
d. If the rate constant of an exponential growth function is increased, its doubling time is decreased.
53
views