Find the domain of the vector-valued function.
r(t) = sin ti + 4 costj + tk
plz help me working
The DOMAIN is all real t
HOWEVER
the RANGE is only from -1 to +1 in i
and -4 to + 4 in j
and all real numbers in k
To find the domain of a vector-valued function, we need to determine the values of t for which the function is defined.
In this case, we have the vector-valued function:
r(t) = sin(t)i + 4cos(t)j + tk
Since all the components of this function involve trigonometric functions (sin and cos) and t, the function is defined for all real values of t. Therefore, the domain of the function is (-∞, ∞).