Exam Prep

Question 1

For a monotone function on an open interval, the set of discontinuities is

Answer 1

Either finite or countable Infinite

Question 2

For Monotonic f on open interval (a,b), all discontinuities are

Answer 2

Jump discontinuities

Question 3

define left and right limits

Answer 3

Question 4

As x-> 0 , for n>m>0

Answer 4

Question 5

As x-> inf, for n>m>a>0

Answer 5

Question 6

At local extrema of a function f, f does not have to

Answer 6

Be differentiable

Question 7

Rolle’s theorem

Answer 7

f€C[a,b] and f(a) = f(b)
If f is differentiable on (a,b)
=>
Exists c€ (a,b) where f’(c) =0

Question 8

MVT

Answer 8

f€C[a,b]
f€C^1(a,b)
=>
Exists c€(a,b) st
f’(c) = (f(b)-f(a))/(b-a)

Question 9

How to prove that f is NOT uniformly continuous on Δ

Answer 9

Question 10

State what it means for f to be analytic on an open interval I

Answer 10

Question 11

Answer 11

Question 12

Integral of 1/x converges if? For (1,inf)

Answer 12

Question 13

Integral of 1/xlogx converges if

Answer 13

Question 14

Integral of 1/x converges for (0,1) if

Answer 14

Question 15

Integral of 1/x|logx| converges for (0,1/2) if

Answer 15

Question 16

Integral of 1/x converges for (0,inf) if?

Answer 16