Calculate the limit of a vector? Find $$~\lim_{t→0} f (t)~$$ if it exists $$f(t) = \dfrac{\sin t}{2t} ~\hat i + \, e^{2 t}~\hat j + \dfrac{t^2}{e^{t}}~\hat k ~.$$ When I plug in $~t\to 0~$ for $~f(t)~$, I get $0+j+0...--prophetes.ai

Calculate the limit of a vector? Find $$~\lim_{t→0} f (t)~$$ if it exists $$f(t) = \dfrac{\sin t}{2t} ~\hat i + \, e^{2 t}~\hat j + \dfrac{t^2}{e^{t}}~\hat k ~.$$ When I plug in $~t\to 0~$ for $~f(t)~$, I get $0+j+0$. But the answer is $\left( \frac{1}{2} ~\hat i + ~\hat j\right)$. Could someone tell me where I have made grievous mistake?

Note that $$ \lim_{t\to0}\frac{\sin t}{2t} = \frac{1}{2}. $$ (Think L'Hopital's!)