Compose a module that implements the hyperbolic trigonometric functions based on the definitions sinh(x) = (e...
Compose a module that implements the
hyperbolic trigonometric functions based on the
definitions sinh(x) = (e – e ) / 2 and cosh(x) = (e +
e ) / 2, with tanh(x), coth(x), sech(x), and csch(x)
defined in a manner analogous to the standard
trigonometric functions.
In Python
Homework Answers
`Hey,
Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.
Note: Brother sometimes while uploading on HomeworkLib the indentations change. So, I request you to verify it with screenshot once. This is the link where I have saved the code too
https://trinket.io/python3/a87af714e8
import numpy as np
def my_sinh(x):
return (np.exp(x)-np.exp(-x))/2.0
def my_cosh(x):
return (np.exp(x)+np.exp(-x))/2.0
def my_tanh(x):
return my_sinh(x)/my_cosh(x);
def my_coth(x):
return my_cosh(x)/my_sinh(x);
def my_sech(x):
return 1.0/my_cosh(x);
def my_csch(x):
return 1.0/my_sinh(x);
print(my_csch(1));
Kindly revert for any queries
Thanks.
Add Answer to:
Compose a module that implements the
hyperbolic trigonometric functions based on the
definitions sinh(x) = (e...
' ' 3. The hyperbolic trigonometric functions are defined by sinh(t) , The following identities m...
' ' 3. The hyperbolic trigonometric functions are defined by sinh(t) , The following identities might be helpful in the following problem. You should convince yourself that they are true, but you are not required to write up proofs/derivations cosh2 1-sinh2に1, cosh2 1 + sinh2にcosh(21), cosh 1 -sinh 1-cosh 1 sinh 1, dl dl (a) For a real number t, define sinh-1に1n(t + Vt2 + 1) Show that sinh(t) is the unique eaber u such that sinhu t (b) Use...
Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing...
Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on their domains. B. sinh x and cosh x are increasing on their domains. C. cosh x and sech x are increasing on their domains. D. sinh x and tanh x are increasing on their domains.
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its appli...
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only...
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x)...
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x) = cosh(x), cosh? (x) – sinh? (x) = 1. Compute the Wronskian of cosh(2) and sinh(2). Using your question 1's answer, cosh() and sinh(x) are linearly independent on R True False
In class we discussed the relationship between the hyperbolic functions and a hyperbola then showed that it is analogou...
In class we discussed the relationship between the hyperbolic functions and a hyperbola then showed that it is analogous to that of the trigonometric functions and a circle a. Derive an analogue to the Pythagorean Identities (cos2 x + sin2 x 1, etc. ) for the hyperbolic functions hint: Which hyperbola and which circle? (this will give you the relationship between cosh x and sinh x and the others are then easily found as they were in the case of...
Please solve all three. Thank you very much 5. (a) Let a be a constant (we...
Please solve all three. Thank you very
much
5. (a) Let a be a constant (we can write “a ER” to mean “a is a real number”). Verify that y(x) = ci cos(ax) + C2 sin(ax) is a solution for y" = -a’y, where C1,C2 ER. (b) Consider the hyperbolic trigonometric functions defined by cosh(x) = et tex 2 ex – e- sinh(x) = * d Show that I cosh(x) = sinh(x) and sinh(x) = cosh(x). (e) Verify that y(x)...
If a body of mass m falling from rest under the action of gravity encounters an...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
10. Find the first derivative with respect to the independent variable for the following functions: (a)...
10. Find the first derivative with respect to the independent variable for the following functions: (a) f(x) = sinh(4x) (b) g(t) = cosh(t) sinh(t). 1 - cosh(r) (c) h(r) = 1 + cosh(r) (d) F(X) = tanh(e). (e) y = sinh--(VT). (Hint: Apply implicit differentiation to sinh(y) = VT.) 11. Use appropriate hyperbolic function substitutions to evaluate the following indef- inite integrals: dc (a) /+) Ke-10) (e)/() dx (b) dar James G., Modern Engineering Mathematics (5th ed.) 2015.: Exercise set...
please use python and provide run result, thank you! click on pic to make it bigger...
please use python and provide run result, thank you!
click on pic to make it bigger
For this assignment you will have to investigate the use of the Python random library's random generator function, random.randrange(stop), randrange produces a random integer in the range of 0 to stop-1. You will need to import random at the top of your program. You can find this in the text or using the online resources given in the lectures A Slot Machine Simulation Understand...
' ' 3. The hyperbolic trigonometric functions are defined by sinh(t) , The following identities might be helpful in the following problem. You should convince yourself that they are true, but you are not required to write up proofs/derivations cosh2 1-sinh2に1, cosh2 1 + sinh2にcosh(21), cosh 1 -sinh 1-cosh 1 sinh 1, dl dl (a) For a real number t, define sinh-1に1n(t + Vt2 + 1) Show that sinh(t) is the unique eaber u such that sinhu t (b) Use...
Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on their domains. B. sinh x and cosh x are increasing on their domains. C. cosh x and sech x are increasing on their domains. D. sinh x and tanh x are increasing on their domains.
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only...
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x) = cosh(x), cosh? (x) – sinh? (x) = 1. Compute the Wronskian of cosh(2) and sinh(2). Using your question 1's answer, cosh() and sinh(x) are linearly independent on R True False
In class we discussed the relationship between the hyperbolic functions and a hyperbola then showed that it is analogous to that of the trigonometric functions and a circle a. Derive an analogue to the Pythagorean Identities (cos2 x + sin2 x 1, etc. ) for the hyperbolic functions hint: Which hyperbola and which circle? (this will give you the relationship between cosh x and sinh x and the others are then easily found as they were in the case of...
Please solve all three. Thank you very
much
5. (a) Let a be a constant (we can write “a ER” to mean “a is a real number”). Verify that y(x) = ci cos(ax) + C2 sin(ax) is a solution for y" = -a’y, where C1,C2 ER. (b) Consider the hyperbolic trigonometric functions defined by cosh(x) = et tex 2 ex – e- sinh(x) = * d Show that I cosh(x) = sinh(x) and sinh(x) = cosh(x). (e) Verify that y(x)...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
10. Find the first derivative with respect to the independent variable for the following functions: (a) f(x) = sinh(4x) (b) g(t) = cosh(t) sinh(t). 1 - cosh(r) (c) h(r) = 1 + cosh(r) (d) F(X) = tanh(e). (e) y = sinh--(VT). (Hint: Apply implicit differentiation to sinh(y) = VT.) 11. Use appropriate hyperbolic function substitutions to evaluate the following indef- inite integrals: dc (a) /+) Ke-10) (e)/() dx (b) dar James G., Modern Engineering Mathematics (5th ed.) 2015.: Exercise set...
please use python and provide run result, thank you!
click on pic to make it bigger
For this assignment you will have to investigate the use of the Python random library's random generator function, random.randrange(stop), randrange produces a random integer in the range of 0 to stop-1. You will need to import random at the top of your program. You can find this in the text or using the online resources given in the lectures A Slot Machine Simulation Understand...
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