hpfan101
  • hpfan101
Let \[g(x)=sgn(\sin x)\] a) Find each of the following limits or explain why it does not exist. i. \[\lim_{x \rightarrow 0^+} g(x)\] ii. \[\lim_{x \rightarrow 0^-} g(x)\] iii. \[\lim_{x \rightarrow 0} g(x)\] iv. \[\lim_{x \rightarrow \pi^-} g(x)\] v. \[\lim_{x \rightarrow \pi^+} g(x)\] \[\lim_{x \rightarrow \pi} g(x)\] b) For which values of a does lim x approaches a for the function, g(x), not exist?
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
where are you stuck at?
hpfan101
  • hpfan101
Well, I'm confused about the one-sided limits. When I substitute 0 into the equation, the sine of 0 is 0. So I'm not sure if I'm doing it right. Because wouldn't it be the same as x approaches 0 from the right or left?
hpfan101
  • hpfan101
I think the fact that it has a sine in the function is what making me confused.

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hpfan101
  • hpfan101
Would we just substitute a value less than 0 to find the limit as x approaches 0 from the left. Like -0.01?
amistre64
  • amistre64
what is your definition of the sgn function?
amistre64
  • amistre64
|dw:1442784418003:dw|
amistre64
  • amistre64
|dw:1442784453858:dw|
amistre64
  • amistre64
sgn(u) = -1 if u < 0 sgn(u) = 0 if u = 0 sgn(u) = 1 if u > 0 sin(x) alternates between -1 and 1 so its composite here will do the same ...
amistre64
  • amistre64
so this question reduces to finding out if the value is approaching -1 or 1 from the given direction and value.
hpfan101
  • hpfan101
The definition of sgn based on the textbook was "signum" (or sign) function.
amistre64
  • amistre64
right, and its value is either -1, 0, or 1 depending on the sign of its argument
amistre64
  • amistre64
sgn(-32.484843) = -1, since the argument is negative sgn(29.1823) = 1, since the argument is positive sgn(0) = 0 since zero is neither positive or negative.
hpfan101
  • hpfan101
Oh, I see. Alright, thank you.
amistre64
  • amistre64
youre welcome

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