Question

Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.

Short answer

Ans:

Step-by-step solution

Step 1. Given information:

Step 2. FInding the limit of a vector function:

Definition of the limit of a vector function

Assume $r\left(t\right)=⟨x\left(t\right),y\left(t\right)⟩$be a vector valued function. The limit of $r\left(t\right)$as $t$approaches $t_0$, denoted by $\underset{t\to t_0}{\lim }r\left(t\right)$is defined by

where $\underset{t\to t_0}{\lim }x\left(t\right),\underset{t\to t_0}{\lim }y\left(t\right)$and $\underset{t\to t_0}{\lim }z\left(t\right)$ exist .

Step 3.

Rewrite the limit,

$=⟨1,0,e⟩$

Therefore,