# Intermediate Value Theorem (IVT)

If $f(x)$ is continuous on a closed interval $[a,b]$, then for every value $M$ strictly between $f(a)$ and $f(b)$, there exists at least one value $c$ such that $f(c)=M$.

Theorem 2: Initial Value theorem

If $f(t)$ is piecewise-continuous and $∫_{0}∣f(t)∣e_{−αt}$ converges for some $α∈R$ then $f(0_{+})=lim_{s→∞}sF(s)$