Theorem of implicit functions help

In summary, the conversation is about a calculus question where the goal is to find dy/dx and d^2y/dx^2 at a specific point, and also derive a formula for d^2x/dy^2 using another given formula. The participants discuss using the theorem of implicit functions to solve the problem and suggest a method of finding the derivatives.
  • #1
caz2bee
1
0
hi guys,
im a little stuck at the moment trying to answer the follwing calculus question, can anyone help me please.

if x=a(theta-sintheta), y=a(theta+sintheta), find dy/dx and d^2y/dx^2 at the point where theta=pi/2.

and given that dy.dx=(dx/dy)^-1, find a fomula for d^2x/dy^2 in terms of dy/dx and d^2y/dx^2.
and verify the formula for y=x^2

i really don't know where to start with this one. :cry: :frown: :rolleyes:
 
Last edited:
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  • #2
Do you know the theorem of implicit functions...?

Daniel.
 
  • #3
you have to first get the dy/d(theta) and dx/d(theta) and then place them like
dy/d(theta) *d(theta)/dx =dy/dx
 

Related to Theorem of implicit functions help

1. What is the theorem of implicit functions?

The theorem of implicit functions is a mathematical concept that states that under certain conditions, a function can be expressed as an implicit equation instead of an explicit equation.

2. What are the conditions for the theorem of implicit functions to hold?

In order for the theorem of implicit functions to hold, the function must be continuously differentiable and the derivative with respect to the dependent variable must be non-zero at the point in question.

3. How is the theorem of implicit functions used in real-world applications?

The theorem of implicit functions is often used in physics and engineering to solve equations that cannot be easily solved explicitly. It also has applications in economics, where it can be used to analyze relationships between variables that are not explicitly defined.

4. Can the theorem of implicit functions be used for multivariable functions?

Yes, the theorem of implicit functions can be extended to multivariable functions, where the implicit equation involves multiple variables.

5. What are the limitations of the theorem of implicit functions?

The theorem of implicit functions can only be applied to functions that satisfy the required conditions and have a unique solution. It also cannot be used to find explicit solutions, as it only expresses the function implicitly.

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