Question

Explain if the limit of the function f(t) exist at t=1 where,

F(t)={ +5 if t<1} 

  {3-3t if t>1}

Answer 1

If $\lim_{t\to1}f(t)$ exists then the limits $\lim_{t\to1+0}f(t)$ and $\lim_{t\to1-0}f(t)$ must exist and be equal.

$\lim_{t\to1-0}f(t)=\lim_{t\to1-0}5=5$

$\lim_{t\to1+0}f(t)=\lim_{t\to1+0}(3-3t)=0$

Since these limits are distinct, the limit $\lim_{t\to1}f(t)$ does not exist.