Find L[f(t)], where: f(t) = { 1, t², 4, if 0 ≤ t < 1, if 1 ≤ t < 2, if t≥ 2.

Suppose that f(2)=1 and f′(x)≤5 for all values of x. Determine a lower bound for f(−2). Determine an upper bound for f(5).

Use FTC I to prove that if |f '(x)| ≤ K for x ∈ [a, b], then |f (x) − f (a)| ≤ K|x − a| for x ∈ [a, b].

Let f be defined by f(q)=3q for q rational and f(t)=t2 for t irrational.. b) is f continuous at 3? prove your answer, remember to prove true you MUST prove it to be true, not use a specific example.