Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Step-by-step explanation:

The given vector function  can be correctly expressed as:

The domain of the given function can be determined by finding the domain of each respective component.

To start with

Not defined, t = -2

Thus, the domain of the first component of the vector =

The 2nd component = sin t

No restriction on t

The 3rd component of the function is ㏑(36 - t²)

Let recall that natural is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

Thus, it satisfies the inequality  -6 < t < 6

The third domain = (-6,6)

Overall;

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

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