Question

the equation x^13 -exp(-x) +x - sin(x)=0 has
a) no real root
b) more than 2 real roots
c) exactly 2 real roots
d) exactly one real root

Answer 1

i dont think u can solve this eqn explicitly...are u allow to use a graphing calculator like the one here http://www.wolframalpha.com/ ? It would be easy if u can...

Answer 2

yes ,,
in this first we have to find its derivative then showing its an increasing function we have to find roots

Answer 3

ah...ok so u found its derivative AND that its an increasing function already right?

Answer 4

yes,but i am not getting it further

Answer 5

well an increasing function means if x increases, y ALWAYS increases n if x decreases, y always decreases.

Answer 6

the answer is exactly one root

Answer 7

yes n do u know why there is exactly one root?

Answer 8

no

Answer 9

Put compare x=0 and x=1, u will see the value of the eqn changes from -ve to +ve, so there must be one root between 0-1. And because it is an increasing function, there will not be any more root.

Answer 10

but why we choose to compare 0 and 1

Answer 11

cuz' those are easy to calculate perhaps?

my true reason is I used wolfram n saw the root between 0 n 1 ;)

Answer 12

ok ,
and if the ion is increation then is it having exactly 1 root?

Answer 13

Sorry I dont understand what this means "if the ion is increation"

Answer 14

sorry its
if function is increasing then is it having exactly one root

Answer 15

sorry - i got a quick bite ;) if the function is increasing n its value changes from -ve to +ve between two x values, then it has one root between the two x values.