anonymous
  • anonymous
Find the limit as x approaches 0 of: x^2 + cosx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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myininaya
  • myininaya
Did you plug in 0? :) This function is continuous at x=0 so you may do so
anonymous
  • anonymous
Why do you do that?
anonymous
  • anonymous
because it is easiest

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anonymous
  • anonymous
if \(f\) is continuous then \(\lim_{x\to a}f(x)=f(a)\)
anonymous
  • anonymous
Okay, but is there another way to do this? Like with identities?
anonymous
  • anonymous
no
anonymous
  • anonymous
How do you know it is continuous?
myininaya
  • myininaya
f(0) exists
myininaya
  • myininaya
and the functions is continuous everywhere
myininaya
  • myininaya
because x^2 is continuous everywhere and cos(x) is continuous everywhere
anonymous
  • anonymous
every function you know that is definded on an interval is continous on its domain
anonymous
  • anonymous
sine, cosine, exp, log, any polynomial, any rationa function etc all continuous on their domains
anonymous
  • anonymous
okay but if it were something like sinx/x it would not be continuous because x is undefined at 0?
anonymous
  • anonymous
even that one is continous on its doman. just happens that the domain does not include zero
anonymous
  • anonymous
limit exists at x = 0, but the function does not, so it is not continous at 0 in order for a functioni to be continuous at a point "a" it must be defined at "a"
anonymous
  • anonymous
okay thanks:)

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