Determine the interval(s) on which the vector-valued function is continuous r(t)=2e^{-t}i+e^{-t}j+\ln(t-1)k

rompentskj

rompentskj

Answered question

2021-11-28

Determine the interval(s) on which the vector-valued function is continuous
r(t)=2eti+etj+ln(t1)k

Answer & Explanation

Thouturs

Thouturs

Beginner2021-11-29Added 12 answers

Step 1
We have to determine the interval on which the vector valued function is continuous.
1) r(t)=2eti+etj+ln(t1)k
Let us break r(t) in parametric equations.
2) kr(t)=a(t)i+b(t)j+c(t)k
Step 2
On compairing equation (10 with (2) we get
a(t)=2et, b(t)=et, c(t)=ln(t1)
for a(t)=(, )
b(t)=(, )
c(t)=ln(t1)
t1>0
t>1
c(t)=(1, )
for r(t)=(1, )

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