Evaluate the limit. Note: two ‘o's make infinity (\propto). \lim_{t arrow

pamangking8

pamangking8

Answered question

2021-12-01

Evaluate the limit. Note: two ‘o's make infinity ().
limtarrow02et,sin(t)3t,(t3)2

Answer & Explanation

Huses1969

Huses1969

Beginner2021-12-02Added 18 answers

Step 1: Analysis
Given:
limtarrow02et,sin(t)3t,(t3)2
Step 2: Solution
If r(x)=f(x),g(x),h(x) is a vector-valued function then,
r(x)=limxarrowcf(x),limxarrowcg(x),limxarrowch(x)
Therefore,
limtarrow02et,sin(t)3t,(t3)2=limtarrow0(2et),limtarrow0(sin(t)3t),limtarrow0(t3)2
limtarrow02et,sin(t)3t,(t3)2=2limtarrow0(et),13limtarrow0(sin(t)t),limtarrow0(t3)2
Using limxarrow0=sinxx=1
limtarrow02et,sin(t)3t,(t3)2=2(e0),1

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