Determine the interval(s) on which the vector-valued function is conti

katelineliseua

katelineliseua

Answered question

2021-11-16

Determine the interval(s) on which the vector-valued function is continuous r(t)=8,t,t3.

Answer & Explanation

breisgaoyz

breisgaoyz

Beginner2021-11-17Added 14 answers

Step 1
To determine:
The interval(s) on which the given vector values function is continuous
r(t)=8,t,t3.
Step 2
Explanation:
The vector-valued function, r(t)=f(t),g(t),h(t) is continuous on the interval if each component function, f(t), g(t), and h(t) are continuous on that interval.
Here r(t)=8,t,t3
So, the function r(t) is continuous when the component functions, 8,t,t3 are continuous.
f(t)=8 is the constant function so it is continuous on the interval ,
The function g(t)=t is the radical function so itis continuous on the interval [0,)
And the function h(t)=t3is the cube root function continuous on the interval ,
So the common interval is [0,)
Therefore the given vector values function (rt) is continuous on the interval [0,)

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