Reference no: EM131010228
Hyperbolic functions are similar to trigonometric functions. Define hyperbolic cosine, denoted cosh(x) as
cosh(x) = (ex + e-x) / 2,
and define hyperbolic sine, denoted sinh(x), as
sinh(x) = (ex + e-x) / 2,
1. Use the definition of cosh(x) and sinh(x) to show that
(cosh(x))2 - (sinh(x))2 = 1.
2. The inverse cosh(x) and sinh(x) arc denoted by arccosh(x) and arcsinh(x). Use implicit differentiation to compute (d/dx) arccosh(x) and (d/dx) arcsinh(x).
3. Use the definition of cosh(x) to verify that
arccosh(x) = In (x + √(x2 - 1)
4. Use the definition of arccosh(x) from 3 to compute (d/dx) arccosh(x). Does this match your answer from 2? Explain.
|
Preceding problem produces corks
: Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately normally distributed with mean 3 cm and standard deviation 0.1 cm.
|
|
Distribution of the diameter of the corks
: A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm.
|
|
Determine the proportion of those who signed the petition
: As part of a curriculum review, the psychology department would like to select a simple random sample of 20 of last year's 140 graduates to obtain information on how graduates perceived the value of the curriculum. Describe two different methods t..
|
|
Proportion of overweight children
: a. Approximately what proportion of overweight children has left atrial diameters less than 25 mm? b. Approximately what proportion of overweight children has left atrial diameters greater than 32 mm?
|
|
Define hyperbolic cosine function
: Hyperbolic functions are similar to trigonometric functions. Define hyperbolic cosine, denoted cosh(x) as cosh(x) = (ex + e-x) / 2, and define hyperbolic sine, denoted sinh(x), as sinh(x) = (ex + e-x) / 2.
|
|
Does living in the south cause high blood pressure
: Does living in the South cause high blood pressure? Data from a group of 6278 whites and blacks questioned in the Third National Health and Nutritional Examination Survey between 1988 and 1994 indicates that a greater percentage of Southerners have..
|
|
What in particular stood out or stick with you
: Read the attach chapters and write 250 word "what in particular stood out/stick with you?" and why
|
|
How certain types of leadership
: You will produce a written report that critically assesses and evaluates your company and it's leadership using Value Systems Theory (vMEME) and all the leadership theories it contains.
|
|
Mean and standard deviation
: The article indicated that 500 FBI agents were required to take a polygraph test. Consider the random variable x = number of the 500 tested who fail. If all 500 agents tested are trustworthy, what are the mean and standard deviation of x?
|