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hpfan101
 one year ago
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?
hpfan101
 one year ago
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?

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.1where are you stuck at?

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Well, I'm confused about the onesided 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
 one year ago
Best ResponseYou've already chosen the best response.0I think the fact that it has a sine in the function is what making me confused.

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Would we just substitute a value less than 0 to find the limit as x approaches 0 from the left. Like 0.01?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what is your definition of the sgn function?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442784418003:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442784453858:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1sgn(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
 one year ago
Best ResponseYou've already chosen the best response.1so this question reduces to finding out if the value is approaching 1 or 1 from the given direction and value.

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0The definition of sgn based on the textbook was "signum" (or sign) function.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1right, and its value is either 1, 0, or 1 depending on the sign of its argument

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1sgn(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
 one year ago
Best ResponseYou've already chosen the best response.0Oh, I see. Alright, thank you.
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