Question

Determine the interval(s) where r(t)=< t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous. And Both r1(t)...

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

And

Both r1(t) = < t2, t4 > and  r2(t) = < t4, t8 > map out the same half parabolic graph.

Notice that both r1(1) = < 1, 1 > and  r2(1) = < 1, 1 >.

However, r'1(1) = < 2, 4 > and  r'2(1) = < 4, 8 >.

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.

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