# Multivariable Calculus Question

• pezzang
In summary, the conversation was about a request for help with math problems involving finding the curvature of a helix, the center and parametric equation of an osculating circle, and components of the acceleration vector at a given point. The recipient of the request suggested asking for an explanation or a simpler problem instead of asking for someone to do the work for them.
pezzang
Hey, I need your help doing some of math problems.

Q) A particle's position at time t is determined by the equation of the helix

r(t) = < cost, sint, t>

Let P be a point with a coordinates (0,1,pie/2).

1. Find the curvature k(t) at any time t.

2. Find the center of the osculating circle at P.

3. Write down teh equation of teh osculating plane and the sphere whose intersection with that plane is the osculating circle.

4. Find a parametric equation of the osculating circle at P.

5. Find the acceleration normal vector and tangential acceleration tension vector components of the acceleration vector at P.

If any of you can do these problems, I would appreciate your help. I started finding curvature but i didn't know how to find the curvature with just the vector equation. I thought i needed y = f(x) equation to find curvature. Can anybody answer this by doing number 1 and so on?

Thank you so much in advance!

sir, you got no responses to this. I apologize for our lack of interest. The reason is your request is essentially for someone to do your work for you. try asking things differently. try asking for an explanation of what is going on. or asking for a simpler problem, or something that invovles your doing some of the work, not asking us to do it for you. for give me, i hope this is useful in future.

Sir? Could be a ma'am.

in that case my apologies to ms pezzang.

## What is multivariable calculus?

Multivariable calculus is a branch of mathematics that deals with functions of more than one variable. It extends the concepts of calculus, such as derivatives and integrals, to functions with multiple independent variables.

## Why is multivariable calculus important?

Multivariable calculus is important in many fields, such as physics, engineering, and economics, where the relationships between multiple variables need to be analyzed. It also provides a foundation for more advanced mathematical topics.

## What are some real-world applications of multivariable calculus?

Some examples of real-world applications of multivariable calculus include predicting the path of a satellite, analyzing the flow of fluids, and optimizing economic models.

## What are the key concepts in multivariable calculus?

The key concepts in multivariable calculus include partial derivatives, multiple integrals, vector calculus, and the gradient, divergence, and curl operators.

## How does multivariable calculus differ from single-variable calculus?

In single-variable calculus, the focus is on functions with only one independent variable. In multivariable calculus, the focus is on functions with multiple independent variables, and the concepts and techniques used are more complex.

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