Q. 30 - Calculus

Question

Find parametric equations for each of the vector-valued functions in Exercises 26–34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

$r\left(t\right)=(3+t)i+(3-\frac{1}{t})j for t>0$

Step-by-Step Solution

Answer

The parametric equation of the vector valued functions $r\left(t\right)=(3+t)i+(3-\frac{1}{t})j for t>0$ is $y=\frac{3x-10}{x-3}$.

And the graph of the function is:

Step 1. Given Information.

The function:

$r\left(t\right)=(3+t)i+(3-\frac{1}{t})j for t>0$

Step 2. Find the parametric equations.

The parametric equations for the given function is:

$$\begin{gathered} x=3+t \\ y=3-\frac{1}{t} \end{gathered}$$

By eliminating t from the other equations, we get,

$y=\frac{3x-10}{x-3}$

Step 3. Graph the function.

The graph of the function is: