dy/dx=sinh(x) A tangent line through the origin has equation y=mx. If it meets the graph at x=a, then ma=cosh(a) and m=sinh(a). Therefore, asinh(a)=cosh(a). Use Newton's Method to solve for a

Maverick Avery 2022-10-23 Answered
d y / d x = sinh ( x ) A tangent line through the origin has equation y = m x. If it meets the graph at x = a, then m a = cosh ( a ) and m = sinh ( a ). Therefore, a sinh ( a ) = cosh ( a ).
Use Newton's Method to solve for a
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Pradellalo
Answered 2022-10-24 Author has 16 answers
You are looking for the zero of function
f ( a ) = a sinh ( a ) cosh ( a )
for which
f ( a ) = a cosh ( a ) and f ( a ) = a sinh ( a ) + cosh ( a )
Since the function is even, you have two symmetric solutions.
What you can notice is that f ( 0 ) = 1, f ( 0 ) = 0 and f ( 0 ) = 1. So, to generate a guess, perform a Taylor expansion around a = 0; this would give
f ( a ) = 1 + a 2 2 + a 4 8 + O ( a 6 )
which is a quadratic in a 2 . So, an estimate is
a 0 = 2 ( 3 1 )
Now, use Newton method which generates as itegrates
a n + 1 = a n f ( a n ) f ( a n ) = a n + 1 a n tanh ( a n )
which should converge very fast.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-08-19
Use newton's method with the specified initial approximation x 1 to find x 3, the third appromizmation to the root of the given equation
x 5 x 1 = 0, x 1 = 1
asked 2022-09-25
To find approximate a we can use Newton's method to approximately solve the equation x 2 a = 0 for x, starting from some rational x 0 .
Newton's method in general is only locally convergent, so we have to be careful with initialization.
Show that in this case, the method always converges to something if x 0 0.
asked 2022-08-14
How many iterations must I do for getting n signs after floating point in calculating square root by Newton's method?
asked 2022-11-19
Using impulse formula, derive p_1 i+p_2 i=p_1 f+p_2 f formula where i-is initial state, f-is the final state after collision. Thanks
asked 2022-09-19
1. If you weigh 140 lbs on Earth, what is your mass in kilograms
2.Using the answer from problem I (hopefully it's correct), determine your weight in Newton's if you were on the moon. Yes, you have to look up something to complete this problem.
3. You measured the mass of a rock to be 355g. What is its weight?
4.You are now holding the rock in your hand from problem 3. What force is the rock on your hand? How much force do you need to exert on the rock to hold in stationary.
asked 2022-09-27
Why the bisection method is slower than Newton's method from a complexity point of view?
asked 2022-07-18
How calculate programs/packages like Matlab, Python/scipy, ...the inverse jacobian for multidimensional Newton's method?
x n + 1 = x n ( J ( x n ) 1 f ( x n )

New questions