Stuck in some vector function problems

[Futurephysicist]

Hi ,i'm a new user to free math help.
I have 2 limit and 2 drivative questions.
Although i know both concepts as well but i don't know how to solve vector function problems(limit and derivative)
Please answer to this questions with a solution and a little bit explanation.
Thanks!

 

[Romsek]

Just use what you know on each component of the vectors.

 

[HallsofIvy]

\(\displaystyle \lim_{x\to a} \left(f(x)\vec{i}+ g(x)\vec{j}+ h(x)\vec{k}\right)= (\lim_{x\to a} f(x))\vec{i}+ (\lim_{x\to a} g(x))\vec{j}+ (\lim_{x\to a} h(x))\vec{k}\).