Question

show that the following equation has at least one solution in the given

Answer 1

x[(cos x)-2x+3=1
Has at least one solution x=1

Answer 2

i dont understand

Answer 3

just check the values on either side :|

Answer 4

let the LHS be a f , give it a name

Answer 5

find the value of f at 0.2 and at 0.3

Answer 6

Put the -1 on the RHS and you have
\[x \cos x - 2x ^{2}+3x =1\]Pull out the common x\[x(\cos x -2x+3)=1\]That equation is x times the bracket =1.
When the bracket is equal to zero, x=1.
cos x- 2x+3=1 if you were to solve it, it would give you a different answer but no need, question asks for one solution only.

Answer 7

whoa whoa!

Answer 8

what

Answer 9

:|

Answer 10

2 intervals

Answer 11

chaguans I thought u were a uni student

Answer 12

u shouldnt be making such mistakes

Answer 13

x( cosx -2x+3) =1

Answer 14

doesnt imply x=1

Answer 15

it must be equal to zero for that to work

Answer 16

Correct way

let f(x) = x cosx -2x^2 +3x

Answer 17

so what do i do?
i use the intermediate value theorem?
i find f(0.2) and f(0.3) if they r of opposite signs that means that thers a solution?

Answer 18

find f(0.2) and f(0.3) , these will have different signs

Answer 19

find f(1.2) and f(1.3) they should be different sign , and the function is continuous for all x , so intermediate value theorm means atleast one zero in the interval.

Answer 20

also, be careful with the trig functions, the calculator has to be in RADIAN mode

Answer 21

can i ask you another question plzz?

Answer 22

might as well

Answer 23

wait I missed the -1 with the function on that other question.

Answer 24

but you should be able to correct it .

Answer 25

what about if i hav an equation and im asked to find the interval containing the solution

Answer 26

then you need to take derivatives, find turning points.

Answer 27

http://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxraGFkZXJtYWlzYXxneDoxNzVmMjhjZDUzMWZiZjg1

Answer 28

q.2, a

Answer 29

?

Answer 30

I cant see it

Answer 31

x-3^-x =0

Answer 32

Think it's x - 3^-x

Answer 33

yeah

Answer 34

You could graph it...

Answer 35

well you can differentiate ( takes a little with that -x ) power

Answer 36

or you could just guess 0 and 1

Answer 37

just by inspection , just try small numbers , they shouldnt expect you to be very accurate.

Answer 38

x=0 , its negative, x=1 , its positive.

the power of having index, just make them zero and the term becomes 1

Answer 39

so the interval is [0,1]

Answer 40

If you rearrange it to x3^x-1 = 0 for solutions,u can see roughly what x must be.

Answer 41

Yes, that's right (and many others, of course).

Answer 42

\[x - 3^{-x} =0\]

just make sure that was what you meant

Answer 43

should use brackets when asking questions

Answer 44

its \[x - 3^{-x}\]

Answer 45

3^-x

Answer 46

thankyou guys i got the idea ,,,

Answer 47

np

Answer 48

Refer to the Mathematica attachment.

Answer 49

oh wow... Thnks alot robtobey :D