Question

Determine the interval(s) where **r(t**)=<
t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous.

And

Both **r _{1}(t)** = < t

Notice that both **r _{1}(1)** = < 1, 1
> and

However, **r' _{1}(1)** = < 2, 4 >
and

Explain why the difference is logical and quantify the difference at t=1.

Determine the interval(s) where **r(t**)=<t − 1
t 2 − 1,2 e 3 t,ln ( t + 5 )> is continuous.

Answer #1

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Two spacecraft are following paths in space given by
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(Use decimal notation. Give your answer to two decimal
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A particle travels along a straight line with a velocity
v=(12−3t^2) m/s , where t is in seconds. When t = 1 s, the particle
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Determine the displacement from t = 0 to t = 7 s.
Determine the distance the particle travels during the time
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The position (in meters) of an object moving in a straight
line
s(t)=√ 3t+1 −2t^2+1
where t is measured in seconds.
(a) Find the average velocity on [0,1].
(b) Find the instantaneous velocity at t=1.
(c) Find the acceleration at t=1.

Determine the length of the curve r(t) = 4i + 2t^2 j + 1/3t^3 k
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1) Find the curvature of the curve r(t)= 〈4+3t,5−5t,4+5t〉 the
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Consider the parameterized motion given by
r(t)=3t^2i-2t^2j+(6-t^3)k.
Where is the object at time t=1? What is the velocity at t=1?
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How far does the object move from 0≤t≤1? Round your
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* r, i, j, and k should all have vector arrows above them

Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for
the points is given by T(x,y,z)=x^2y(1−z), use the Chain Rule to
determine the rate of change of the difference D in the
temperatures the two spacecraft experience at time t=3.
(Use decimal notation. Give your answer to two decimal
places.)

Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for
the points is given by T(x,y,z)=x^2y(8−z), use the Chain Rule to
determine the rate of change of the difference D in the
temperatures the two spacecraft experience at time t=1.
(Use decimal notation. Give your answer to two decimal
places.)

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