anonymous
  • anonymous
A message :)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I find this rather important to some people of openstudy who claim that "anything log,exponentials,arcsin,arccos,arctan...etc can be taken on both sides of an inequality". I hereby state the general principle. Suppose we have an inequality over real x and y: x>y. The above implies f(x)>f(y) if and only if f is a strictly increasing function in [x,y]. The above implies f(x)=y the above statements holds after striking off the "strictly" word.} Now we have the common usage "take log on both sides" whenever required in some inequalities. Observe that f(x)=log(x) is an increasing function in [0,+infty). (Remember you can't "take log on both sides" when there is a negative quantity in atleast one side---see the domain of function definition.) However "take exponential on both sides" is always allowed since the function f(x)=e^x is increasing everywhere {i.e. in (-infty,+infty)}. Even the smallest things you apply to inequalities, like adding one on both sides or subtracting 1 on both sides are possible because the functions f(x)=x+1 and g(x)=x-1 are everywhere increasing. "Taking square roots on both sides" is permissible when both sides have non-negative numbers. Also the sign of the original inequality is preserved since f(x)=sqrt(x) is increasing in [0,+infty). While "taking trigonometric functions" be cautious about the intervals where the function is increasing or decreasing. For x,y in [-pi/2,pi/2] x>y implies sinx>siny and for x,y in [pi/2,3pi/2] x>y implies sinxy implies x>y-1 {x,y are reals}. You also need precautions when doing this i.e. x>y implies f(x)>y only when f(x) has an maps x to a "greater" number say x1 so that x1>x>y i.e. f(z)>z for all z in neighbourhood of x {observe that this operation dilates the inequality; using an operation to make an inequality more stronger than given requires handling with utmost care so that the inequality does not change its sign!}. P.S.:I am sorry as this was not a question as you were expecting, but you may give your suggestions. Since this was not a question, I will give a medal to everyone who comments for about 1 day, after which I will delete this message, unless you persist. Thank you for reading. Good luck!
anonymous
  • anonymous
attchment for better reading..
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anonymous
  • anonymous
lol

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anonymous
  • anonymous
medals for evryone :)
anonymous
  • anonymous
:p
anonymous
  • anonymous
good piece of writing. expand more starting from the line: maps x to a "greater number". like explain it more.
anonymous
  • anonymous
where r u stuck some1?
anonymous
  • anonymous
Haaa?
anonymous
  • anonymous
1 comment = 1 medal ! comment evryone.... :)
anonymous
  • anonymous
OMG SO LONG Medal now.
anonymous
  • anonymous
This speech is longer than Fidel Castro's marathon rants.
anonymous
  • anonymous
what on earth was that?? i didnt understand even a bit :P

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