Exam 1

Question 1

State the Squeeze Theorem

Answer 1

If f(x)≤g(x)≤h(x) is close to x in some interval around c but not at c and
limit x—>c f(x) = L = lim x—> c h(x)

Then,

Limit x—>c g(x) = L

Question 2

State the Intermediate Value Theorem

Answer 2

Suppose f is a continuous on [a,b] and let N be any number between f(a) and f(b), where f(a)≠f(b). Then there exists a number c in (a,b) such that f(c) = N

Question 3

Formal Definition of a Limit

Answer 3

If for each epsilon > 0 there exists a delta >0 such that whenever |x-a|< delta we have |f(x) -L| < epsilon

Question 4

When is a function continuous?

Answer 4

F is continuous at a if f(a) = lim x—> a f(x) is
-f(a) = defined
-lim x—> a f(x) exists
-lim x—> a f(x) = f(a)