# Help with Calculus Homework: Find Tangent Plane, Intuitive Geometric Argument

• Marioqwe
In summary: A geometric argument is an intuitive explanation or justification based on the visual representation of a mathematical concept or problem. In this case, it involves understanding the shape of the surface and how it relates to the tangent plane at a specific point.
Marioqwe

## Homework Statement

1.Find the equation of the tangent plane at p=(0,0) on the surface z=f(x,y)=√(1-x²-y²)

p is a vector.

2.Give an intuitive geometric argument to support the result

## The Attempt at a Solution

So I have no problem finding the equation of the tangent line. I am supposed to use the gradient to find it. But I don't really understand the second question. What is a geometric argument?

Is it correct if I justify my answer by saying that the tangent plane is locally linear at p? Is that a geometric argument?

Somehow, I feel that it is just not enough.

Don't give me the answer please. Just a hind of what it means by "geometric argument."

Thank You

Marioqwe said:

## Homework Statement

1.Find the equation of the tangent plane at p=(0,0) on the surface z=f(x,y)=√(1-x²-y²)

p is a vector.

2.Give an intuitive geometric argument to support the result

## The Attempt at a Solution

So I have no problem finding the equation of the tangent line. I am supposed to use the gradient to find it. But I don't really understand the second question. What is a geometric argument?

Is it correct if I justify my answer by saying that the tangent plane is locally linear at p? Is that a geometric argument?
No. The surface z = f(x, y) = sqrt(1 - x^2 - y^2) represents a geometric figure. Your justification should involve this figure. If you knew what this figure was, you could work out the equation of the tangent plane in your head, without the use of calculus.
Marioqwe said:
Somehow, I feel that it is just not enough.

Don't give me the answer please. Just a hind of what it means by "geometric argument."

Thank You

Thank you very much. I'm still struggling with geometric interpretations but this surely helped.

You're welcome.

## 1. What is a tangent plane?

A tangent plane is a flat surface that touches a curve or surface at exactly one point. It is used to approximate the curve or surface at that point.

## 2. How do I find the equation of a tangent plane?

To find the equation of a tangent plane, you need to know the coordinates of the point where the plane touches the curve or surface and the gradient vector at that point. Then, you can use the formula: z - z0 = fx(x - x0) + fy(y - y0), where (x0, y0, z0) is the point and fx and fy are the partial derivatives of the function at that point.

## 3. What is an intuitive geometric argument?

An intuitive geometric argument is a way of explaining a concept or solving a problem using visual aids and geometric reasoning. It helps to understand complex mathematical concepts by relating them to familiar geometric shapes and principles.

## 4. How can I use an intuitive geometric argument to find a tangent plane?

You can use an intuitive geometric argument to find a tangent plane by visualizing the curve or surface and its tangent plane at a specific point. By using geometric reasoning, you can determine the slope of the tangent plane and use it to find the equation of the plane.

## 5. What are some common applications of tangent planes?

Tangent planes have various applications in different fields of science and engineering. Some common applications include approximating the behavior of curves and surfaces, optimizing functions, and understanding the motion and forces of objects in physics and engineering problems.

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