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Solve for 0, then factor.

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

thought that was a typo lol

its called the discriminant

Same here.

soooo close......

b^2-4ac

but how does discriminant help ?

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

x^2 = -2^x +2
square root both sides?

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

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

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

ahh..got ya !!!

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

by taking the square root

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

if you wanna limit your self to even values of x

but there is no domain given in the question

meanwhile
i checked on wolfram alpha

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

they had a graph which cuts on two points

the latter one

maybe log rules would help

would you know guys what is uniform continuity?

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) ??

uniform?... id have to look it up

ok

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

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

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

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

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

so u think graph would be enough?

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

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

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

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

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

how to write pi as a symbol on computer?

on any computer? or in here?

any computer

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

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

hey let me check that one ...thanx

П lol

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

ППППППППППП hhahah

Пп hehehe

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

pi/3 = 60 degrees.....
is [sqrt(3+2cos(x)) - 2] / ln(1+sin(3x)) right?

exactly

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

sqrt(4) - 2 0
--------- = ---
ln(1) 0
I see the dellima

the derivative of each would be....

Dx(ln(x)) = 1/x
Dx(ln(1+sin(3x))) = 3cos(3x)/1+sin(3x)
the reciprocal of that is what youll need

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

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

yes i was also somewhere there

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

i have got 1/4sqrt3

same thing, rationalize your denominator

sqrt(3)/4(3)

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

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

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

thanx :)

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