Theorems

Question 1

Intermediate Value Theorem

Answer 1

If a function is continuous and, for example, there is an interval [2,6] where f(2) = 3 and f(6)=9, the value f(c)=7 must exist on that interval. It is useful for determining the minimum number of zeros there must be on an interval.

Question 2

Squeeze (Sandwich Theorem)

Answer 2

If a function g(x) < f(x) > h(x) and the
lim x->c g(x) = lim x->c h(x)
then the lim x->c f(x) will be equal to that