A curve c is defined by the parametric equations xt24t 1 and yt3


a curve c is defined by the parametric equations xt24t 1 and yt3

There are many benefits to using parametric equations, but one of the biggest is that they can be used to define a curve. This is because parametric equations define a curve by specifying a set of points that the curve passes through. This means that you can use parametric equations to define any kind of curve, from a straight line to a more complicated one.

the domain of c is the set of all real numbers

The domain of c is the set of all real numbers

the range of c is the set of all real numbers

The range of c is the set of all real numbers such that xt24t 1 and yt3.

the curve c is a graph of a function

A curve c is defined by the parametric equations xt24t 1 and yt3. The curve c is the graph of a function. The function is a polynomial function. The degree of the polynomial function is two. The leading coefficient of the polynomial function is one. The roots of the polynomial function are two and three.

the function is continuous

A curve c is continuous if given any two points on the curve, there exists a smooth curve that connects those two points. A simple way to think of this is that a continuous curve can be drawn without lifting your pencil from the paper.

the function is differentiable

Differentiability of a function at a point is a measure of how well the function can be approximated by a linear function near that point. A function is said to be differentiable at a point if there exists a linear function that provides a good approximation to the function near that point. In order for a function to be differentiable, it must be continuous at the point in question. A function that is not continuous at a point cannot be differen

the curve c is the graph of a function that is one-to-one

A curve c is defined by the parametric equations xt24t 1 and yt3 . The curve c is the graph of a function that is one-to-one. The domain of the function is the set of all real numbers t such that t 1 and the range of the function is the set of all real numbers t such that t 3.

the function is invertible

This means that the function is one-to-one, or that for every y-value there is only one x-value. This also means that the curve c is the graph of a function that is one-to-one.

the inverse function is continuous

To show that the inverse function is continuous, we need to show that given any , there exists such that whenever . We also need to show that the inverse function is differentiable at every point in its domain. We will do this by showing that the inverse function has a continuous derivative.

the inverse function is differentiable

If a function is one-to-one, then its inverse function is also one-to-one. Therefore, the inverse function of a one-to-one function is also a function. In addition, the inverse function of a differentiable function is also differentiable.


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