Asymptotic relations for equations Euler-Bernoulli

[Felesinho]

Homework Statement

I need help with asymptotic relations of the equation below
x=f(y) with f(y)=0
I not know how to address the problem

Homework Equations

σ_zz={β³∇⁴h(x,y) if x<f(y)
0 if x>f(y)

The Attempt at a Solution

The solutions is
σ_zz=n(y)/√(∏(f(y)-x))+o(√(f(y)-x) if x→f(y)^-

 

[mighty2000]

0 if x>f(y)-

Dear forum post author,

Thank you for reaching out for help with your problem. Asymptotic relations can be tricky, but I will do my best to explain them to you.

First, let's define some terms. Asymptotic relations describe the behavior of a function as one of its variables approaches a certain value or infinity. In this case, we are looking at the function x=f(y) and how it relates to the variable x as it approaches the value of f(y).

Based on the equations you provided, it looks like you are dealing with a piecewise function. This means that the function has different rules or equations for different intervals of the input variable. In this case, we have two intervals: x<f(y) and x>f(y).

For the interval x<f(y), the equation for σzz is β3∇4h(x,y). This means that as x approaches values less than f(y), the value of σzz will also approach this equation.

For the interval x>f(y), the equation for σzz is 0. This means that as x approaches values greater than f(y), the value of σzz will approach 0.

Now, for the solutions you provided, it looks like you are trying to find the behavior of σzz as x approaches f(y) from the left side (x→f(y)-). In this case, the first solution is n(y)/√(∏(f(y)-x))+o(√(f(y)-x)). This means that as x approaches f(y) from the left, the value of σzz will approach n(y)/√(∏(f(y)-x)), which is the equation for σzz in the interval x<f(y). The second solution, 0, is for when x actually equals f(y).

I hope this helps you understand asymptotic relations and how they apply to your problem. If you have any further questions or need clarification, please don't hesitate to ask. Good luck with your work!