Domains Find the domain of the following vector-valued function. r(t) =\cos

uneskovogl5

uneskovogl5

Answered question

2021-11-29

Domains Find the domain of the following vector-valued function.
r(t)=cos2ti+etj+12tk

Answer & Explanation

Fearen

Fearen

Beginner2021-11-30Added 15 answers

Step 1
The domain of a vector-valued function is the intersection of the domains of its component functions. It is the set of all values of t for which the vector-valued function is defined.
Step 2
We are given the vector valued function: r(t)=cos2ti+etj+12tk with three component functions of variable 't'.
Step 3
We consider the domain of functions of individual components as follows:
For cos2t domain is(,)
For et domain is[0,)
For 12t domain is(,0)(0,)
Step 4
The domain of original function r(t) is the intersection of these domains.
Thus the domain is (0,).
Step 5
Answer:
The domain is (0,).

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