   Chapter 13.1, Problem 6E

Chapter
Section
Textbook Problem

# Find the limit.6. lim t → ∞ 〈 t e − t ,   t 3  + ​  1 2 t 3  - ​  1 ,   t  sin  1 t 〉

To determine

To find: Limit of vector function tet,t3+t2t31,tsin1t .

Explanation

Formula used:

Write the expression for vector function r(t) .

r(t)=f(t),g(t),h(t) (1)

Here,

f(t) , g(t) , and h(t) are component functions of r.

Write the expression for limit of vector function (limtar(t)) .

limtar(t)=limtaf(t),limtag(t),limtah(t) (2)

Compare the vector function tet,t3+t2t31,tsin1t with equation (1).

f(t)=tetg(t)=t3+t2t31h(t)=tsin1t

Substitute tet,t3+t2t31,tsin1t for r(t) , tet for f(t) , t3+t2t31 for g(t) , tsin1t for h(t) , and for a in equation (2),

limttet,t3+t2t31,tsin1t=limttet,limtt3+t2t31,limt<

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