Key to "Domains Find the domain of the following vector-valued..."

impresijuzj

Answered question

2021-11-26

Domains Find the domain of the following vector-valued function.

r (t) = \frac{2}{t - 1} i + \frac{3}{t + 2} j

Answer & Explanation

Forneadil

Beginner2021-11-27Added 18 answers

Data analysis
To find the domain of the vector valued function.
Given vector function,
$r (t) = \frac{2}{t - 1} i + \frac{3}{t + 2} j$
Domain of vector function
The domain of a vector function is the values of vector function parameter for which the components of vector function are defined.
Here, 't' is the function parameter and coefficients of i and j are the components.
Horizontal component is defined if,
$\frac{2}{(t - 1)}$ is defined for all the values of 't' in real excluding $t = 1$ .
As when $t = 1$ , component ( $\frac{1}{2}$ ) which is undefined.
Vertical component is defined if,
$\frac{3}{(t + 2)}$ is defined for all the values of 't' in real excluding $t = - 2$ .
As when $t = - 2$ , component $= \frac{3}{0}$ which is undefined.
Hence, Domain of $r (t) = {t ∣ R - {- 2, 1}}$
Where R is real numbers.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 2

Didn't find what you were looking for?