Unit 8 Math Quiz

Question 1

Limit Existence Theorem

Answer 1

The general limit only exist when the left and right hand limits equal each other

Question 2

Substitution Theorem

Answer 2

If f is a polynomial or a rational function, then
lim x->c f(x) = f(c)

Question 3

Squeeze Theorem

Answer 3

if g(x) ≤ f(x) ≤ h(x)
and lim x-> c g(x) = L
and lim x-> c h(x) = L

then
lim x-> c f(x) = L

Question 4

What is a continuous function

Answer 4

A function is continuous if its domain is an interval and it is continuous at every point of that interval

Question 5

Conditions for a continuous function

Answer 5

1. f(a) exists
2. lim f(x) x->a exists
3. lim f(x) x->a = f(a)

Question 6

The two-sided limit exists but the limit does not equal the function value

Answer 6

Removable discontinuity

Question 7

The two one-sided limits exist but are not equal

Answer 7

Jump discontinuity

Question 8

At least one of the one sided limits goes to ∞ or -∞

Answer 8

Infinite discontinuity

Question 9

Intermediate Value Theorem

Answer 9

If a function f is continuous on a closed interval [a, b] and f(a) does not equal f(b) then for every value k between f(a) and f(b) there is at least one value c in the open interval (a,b) such that f(c) = k

Question 10

One sided limit DNE?

Answer 10

Plug into calc. Should be infinity or negative infinity.