Question

Show that the equation 2^x = 2 − x^2
has at least two real roots

Answer 1

Solve for 0, then factor.

Answer 2

use the determinate..i think its called of the quad formula.... if its 0 only 1 root, if it (+) 2 roots, it its (-) imaginary roots

Answer 3

but its 2^x an exponential fuction...so how to use quadratic here ?

Answer 4

thought that was a typo lol

Answer 5

its called the discriminant

Answer 6

Same here.

Answer 7

soooo close......

Answer 8

b^2-4ac

Answer 9

but how does discriminant help ?

Answer 10

\[-x^2+2^x -2 = 0\]

Answer 11

x^2 = -2^x +2

square root both sides?

Answer 12

x = +-sqrt(-2^x +2)

Answer 13

sry but i m still in a fix ....jeezzzzz

Answer 14

that doesnt tell you the roots, but it might show that there are 2 of them :)

Answer 15

ahh..got ya !!!

Answer 16

hey but the roots can be complex by taking the roots???

Answer 17

by taking the square root

Answer 18

roots can be complex and most are... but the only one to concern yourself with are the "real" roots

Answer 19

yes...when it was +- sqrt( 2- 2^x). that does not show that v r gonna get two real roots which is the question asking for?

Answer 20

if you wanna limit your self to even values of x

Answer 21

but there is no domain given in the question

Answer 22

meanwhile
i checked on wolfram alpha

Answer 23

oh wait... is it (-2)^x or -(2^x)??

Answer 24

they had a graph which cuts on two points

Answer 25

the latter one

Answer 26

maybe log rules would help

Answer 27

would you know guys what is uniform continuity?

Answer 28

log(2^x) = log(2-x^2)

x log(2) = log(2-x^2)

log(2) = log(2-x^2)^1/x

2 =xroot(2-x^2) ??

Answer 29

uniform?... id have to look it up

Answer 30

ok

Answer 31

f(x) = sin x is continuous on R. Is it
uniformly continuous on R?

Answer 32

id vote yes, its periodic, repetitive, and constantly the "same"

Answer 33

if "x" is a fraction that gets us back to integer exponents with the first question....

Answer 34

http://www.wolframalpha.com/input/?i=2^x+%3D+2+%E2%88%92+x^2 check out that one for me plsssssss

Answer 35

..... yeah.....thats correct :)

Answer 36

so u think graph would be enough?

Answer 37

the graph itself is visual proof, the mathematical proof seems a but difficult to reach.

Answer 38

yes...and the second question like you said or is there any better way?

Answer 39

if you graph the sin function, it sounds as if it would fit a "uniform" continuity.

Answer 40

yes...thank you.... can i ask you anything else or i m just pissing u off :(

Answer 41

lol.... you can ask....i might not have an answer tho :)

Answer 42

how to write pi as a symbol on computer?

Answer 43

on any computer? or in here?

Answer 44

any computer

Answer 45

its the ascii code 227 i think, there should also be a character keyboard in your menu that will bring up a virtual keyboard to find it on

Answer 46

yeah mayb in microsoft word ...they might have it ...thanx

Answer 47

programs..accessories....system tools....character maap is where mine is

Answer 48

hey let me check that one ...thanx

Answer 49

П lol

Answer 50

hey u got that...i might copy it n save it on word ...lol

Answer 51

ППППППППППП hhahah

Answer 52

Пп hehehe

Answer 53

lim x->pi/3 ((3+2cosx)^1/2 - 2) / ln (1+sin3x) ??? whats ur views on that one?

Answer 54

pi/3 = 60 degrees.....

is [sqrt(3+2cos(x)) - 2] / ln(1+sin(3x)) right?

Answer 55

exactly

Answer 56

sqrt(3+2cos(60)) - 2 sqrt(3 + 2(1/2)) - 2
------------------- = -----------------
ln(1+sin(180)) ln(1+0)

Answer 57

but thats a limit question ...plugging in the values making it 0/0

Answer 58

sqrt(4) - 2 0
--------- = ---
ln(1) 0

I see the dellima

Answer 59

the derivative of each would be....

Answer 60

Dx(ln(x)) = 1/x

Dx(ln(1+sin(3x))) = 3cos(3x)/1+sin(3x)

the reciprocal of that is what youll need

Answer 61

Dx(sqrt(3+2cos(x))-2) = -sin(x)/sqrt(3+2cos(x))

Answer 62

-sin(x) (1+sin(3x))
----------------------
sqrt(3+2cos(x)) (3cos(3x)

Answer 63

yes i was also somewhere there

Answer 64

-sqrt(3) sqrt(3)
--------- = -------- is what I get
2(3)(-1)(2) 12

Answer 65

i have got 1/4sqrt3

Answer 66

same thing, rationalize your denominator

Answer 67

sqrt(3)/4(3)

Answer 68

got ya !!! u must b a teacher for sure ... aren't u ?

Answer 69

lol ..... nope, just an unemployed carpenter

Answer 70

wtf??? impossible ...to me u r a GREAT TEACHER !!!! and more of a great human being

Answer 71

thanx :)

Answer 72

u have been so helpful...these questions were all for my next week homwork assignment...now i m so relaxed...thanx bro....really appreciate ur help

Answer 73

Refer to the attachment.