anonymous
  • anonymous
Show that the equation 2^x = 2 − x^2 has at least two real roots
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Solve for 0, then factor.
amistre64
  • amistre64
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
anonymous
  • anonymous
but its 2^x an exponential fuction...so how to use quadratic here ?

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amistre64
  • amistre64
thought that was a typo lol
myininaya
  • myininaya
its called the discriminant
anonymous
  • anonymous
Same here.
amistre64
  • amistre64
soooo close......
myininaya
  • myininaya
b^2-4ac
anonymous
  • anonymous
but how does discriminant help ?
anonymous
  • anonymous
\[-x^2+2^x -2 = 0\]
amistre64
  • amistre64
x^2 = -2^x +2 square root both sides?
amistre64
  • amistre64
x = +-sqrt(-2^x +2)
anonymous
  • anonymous
sry but i m still in a fix ....jeezzzzz
amistre64
  • amistre64
that doesnt tell you the roots, but it might show that there are 2 of them :)
anonymous
  • anonymous
ahh..got ya !!!
anonymous
  • anonymous
hey but the roots can be complex by taking the roots???
anonymous
  • anonymous
by taking the square root
amistre64
  • amistre64
roots can be complex and most are... but the only one to concern yourself with are the "real" roots
anonymous
  • anonymous
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?
amistre64
  • amistre64
if you wanna limit your self to even values of x
anonymous
  • anonymous
but there is no domain given in the question
anonymous
  • anonymous
meanwhile i checked on wolfram alpha
amistre64
  • amistre64
oh wait... is it (-2)^x or -(2^x)??
anonymous
  • anonymous
they had a graph which cuts on two points
anonymous
  • anonymous
the latter one
amistre64
  • amistre64
maybe log rules would help
anonymous
  • anonymous
would you know guys what is uniform continuity?
amistre64
  • amistre64
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) ??
amistre64
  • amistre64
uniform?... id have to look it up
anonymous
  • anonymous
ok
anonymous
  • anonymous
f(x) = sin x is continuous on R. Is it uniformly continuous on R?
amistre64
  • amistre64
id vote yes, its periodic, repetitive, and constantly the "same"
amistre64
  • amistre64
if "x" is a fraction that gets us back to integer exponents with the first question....
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=2^x+%3D+2+%E2%88%92+x^2 check out that one for me plsssssss
amistre64
  • amistre64
..... yeah.....thats correct :)
anonymous
  • anonymous
so u think graph would be enough?
amistre64
  • amistre64
the graph itself is visual proof, the mathematical proof seems a but difficult to reach.
anonymous
  • anonymous
yes...and the second question like you said or is there any better way?
amistre64
  • amistre64
if you graph the sin function, it sounds as if it would fit a "uniform" continuity.
anonymous
  • anonymous
yes...thank you.... can i ask you anything else or i m just pissing u off :(
amistre64
  • amistre64
lol.... you can ask....i might not have an answer tho :)
anonymous
  • anonymous
how to write pi as a symbol on computer?
amistre64
  • amistre64
on any computer? or in here?
anonymous
  • anonymous
any computer
amistre64
  • amistre64
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
anonymous
  • anonymous
yeah mayb in microsoft word ...they might have it ...thanx
amistre64
  • amistre64
programs..accessories....system tools....character maap is where mine is
anonymous
  • anonymous
hey let me check that one ...thanx
amistre64
  • amistre64
П lol
anonymous
  • anonymous
hey u got that...i might copy it n save it on word ...lol
anonymous
  • anonymous
ППППППППППП hhahah
amistre64
  • amistre64
Пп hehehe
anonymous
  • anonymous
lim x->pi/3 ((3+2cosx)^1/2 - 2) / ln (1+sin3x) ??? whats ur views on that one?
amistre64
  • amistre64
pi/3 = 60 degrees..... is [sqrt(3+2cos(x)) - 2] / ln(1+sin(3x)) right?
anonymous
  • anonymous
exactly
amistre64
  • amistre64
sqrt(3+2cos(60)) - 2 sqrt(3 + 2(1/2)) - 2 ------------------- = ----------------- ln(1+sin(180)) ln(1+0)
anonymous
  • anonymous
but thats a limit question ...plugging in the values making it 0/0
amistre64
  • amistre64
sqrt(4) - 2 0 --------- = --- ln(1) 0 I see the dellima
amistre64
  • amistre64
the derivative of each would be....
amistre64
  • amistre64
Dx(ln(x)) = 1/x Dx(ln(1+sin(3x))) = 3cos(3x)/1+sin(3x) the reciprocal of that is what youll need
amistre64
  • amistre64
Dx(sqrt(3+2cos(x))-2) = -sin(x)/sqrt(3+2cos(x))
amistre64
  • amistre64
-sin(x) (1+sin(3x)) ---------------------- sqrt(3+2cos(x)) (3cos(3x)
anonymous
  • anonymous
yes i was also somewhere there
amistre64
  • amistre64
-sqrt(3) sqrt(3) --------- = -------- is what I get 2(3)(-1)(2) 12
anonymous
  • anonymous
i have got 1/4sqrt3
amistre64
  • amistre64
same thing, rationalize your denominator
amistre64
  • amistre64
sqrt(3)/4(3)
anonymous
  • anonymous
got ya !!! u must b a teacher for sure ... aren't u ?
amistre64
  • amistre64
lol ..... nope, just an unemployed carpenter
anonymous
  • anonymous
wtf??? impossible ...to me u r a GREAT TEACHER !!!! and more of a great human being
amistre64
  • amistre64
thanx :)
anonymous
  • anonymous
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
anonymous
  • anonymous
Refer to the attachment.

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