anonymous
  • anonymous
Find the constant such that f(x)= {-4*((sin x)/(x)), x<0 -------{a + 10x, x>=0 is continuous on the entire real line. a)4 b)-4 c)-10 d)10 e)1 **I know that the answer is -4(B), but I need to know how to get it**
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Help please, I have test corrections
anonymous
  • anonymous
Use this to take a left sided limit. \[\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1\] Then take a limit of the right side approaching 0 of \(a+10x\). The limits have to be equal to each other and f(0) for f(x) to be continuous.
anonymous
  • anonymous
@peachpi how is sin x/x = 1? that was what stumped me

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anonymous
  • anonymous
(sin x)/x isn't 1. The limit approaching 0 is. \[\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1\] and \[\lim_{x \rightarrow 0}\frac{ 1-\cos x }{ x }=0\] are two limits you need to be able to recognize on sight. I'll see if I can find links to proofs.
anonymous
  • anonymous
For the sine limit: http://math.ucsb.edu/~jcs/SqueezeTheorem.pdf For the cosine limit: http://math.hws.edu/~mitchell/Math130F12/tufte-latex/TrigLimits.pdf

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