Question

How to resolve this limit from Vector Calculus?

`lim_( t → 0) ((t^2-1)/(t-1), (5t-1)/(t+1),(2e^(t-1)-2)/(t-1))`

Answer 1

`(1,-1,2-2/e)`

Explanation:

Just consider the limit of each component:

`\lim_{t\to 0} {t^2-1}/{t-1} = \frac{0^2-1}{0-1} = \frac{-1}{-1} = 1`

`\lim_{t\to 0} {5t-1}/{t+1} = \frac{5*0-1}{0+1} = \frac{-1}{+1} = -1`

`\lim_{t\to 0} {2e^{t-1}-2}/{t-1} = \frac{2e^{0-1}-2}{0-1}=\frac{2/e-2}{-1} = 2-2/e`