Question

Prove that the function y =(x^4 - x^3 + x^2 - x -2)/(x^2 + x + 1)
crosses the x-axis somewhere between -1 and 1

Answer 1

and the unit we are workin on is derivatives

Answer 2

when x=1, y=-2/3
when x=-1, y=2.
Therefore, there must be y=0 between -1<=x<=1

Answer 3

but that might be a discontinuity

Answer 4

I believe you want to use the intermediate value theorem. When you plug in x = -1, you get a positive answer, and when you plug in x = 1 you get a negative answer.

Because the function is continuous between -1 and 1, you can use the intermediate value theorem to say there must be some point inbetween where the value of the function is 0.

Answer 5

I think because they are polynomials they are continuous for all x

Answer 6

how do you know it's continuous there

Answer 7

x^2+x+1 = (x+1/2)^2 + 3/4, and is always larger than 3/4

Answer 8

there are no points of discontinuity in the reals. the values of x that make x^2+x+1 =0 are complex (cube roots of unity to be exact)

Answer 9

o ok

Answer 10

have you done the maple part of the assignment yet?

Answer 11

im on part b) it wont work for me tho

Answer 12

what did you graph?

Answer 13

f(x)= x^2-1-sinx

Answer 14

yeah that's what I did too

Answer 15

just copy and pasted what they did in the pre lab for part b but it didnt work

Answer 16

that's what I did too, even the interval for the first one was the same. It worked for me

Answer 17

it wouldnt solve for f(a) and f(d)

Answer 18

I used the loop to solve that part. Do you think we're supposed to do all 10 iterations?

Answer 19

no i just copy and pasted the loop part

Answer 20

did you assign an a and a b variable before running the loop?

Answer 21

ya then (a+b)/2=d

Answer 22

you don't need to do a d since that is already in the loop

Answer 23

try going through each of your expression statements and pressing enter on all of them again. Sometimes that works when it is messing up. or copy and paste the loop in again

Answer 24

k ya i tried everything- how is the rest of your assignment?

Answer 25

which one?

Answer 26

number 4 i was havin trouble with- the other ones look like they are pretty much from our notes tho

Answer 27

I've actually just started lol. I just finished number one when I read your question.

Answer 28

ya its not a polynomial so i dunno how to prove its continuous

Answer 29

for#1

Answer 30

Well the bottom will never be 0 because of the +1 right

Answer 31

just could be factored

Answer 32

quadratic formula

Answer 33

you still need to keep in mind the original restrictions on the function. The graph of x^2+x+1 is always positive. So the function would be defined anywhere.

Answer 34

ok so its simple then-on to #2

Answer 35

I haven't even really started that one, but I never did linearization in class

Answer 36

i know eh - they really need to stop screwin with us and stick to what they taught us

Answer 37

at least the last one was pretty easy, and from what you say this one is pretty straight forwards to right?

Answer 38

the one before that was really hard though and there are always those problems that you've never seen before too

Answer 39

ya man number 2 and 3 are pretty easy

Answer 40

what about 5 and 6?

Answer 41

5 looks hard but 6 looks like its from our notes

Answer 42

actually i dont know how to do 3

Answer 43

for a you take the lim as x-> +inf and whatever that is is the asymptote right?
for b we have that equation of the tangent line formula
for c you can use a online graphing thing to get a better idea of what it should look like

I think, just from a glance through anyways. I'll get there after number 2 though. Maybe I'll just do it tomorrow lol

Answer 44

ya me too haha- last resort ill just come on here and post everything

Answer 45

sometimes I've come on here and noticed you already asked the question I was going to ask and have already got an answer lol

Answer 46

ya man just check mine first- i dont think its cheating cuz im learning too

Answer 47

I think it's the same as if we went and asked a TA. People on here are just more convenient to get help from

Answer 48

k im done for tonite

Answer 49

same lol, night!

Answer 50

night