where are you stuck at?
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?
I think the fact that it has a sine in the function is what making me confused.
Would we just substitute a value less than 0 to find the limit as x approaches 0 from the left. Like -0.01?
what is your definition of the sgn function?
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 ...
so this question reduces to finding out if the value is approaching -1 or 1 from the given direction and value.
The definition of sgn based on the textbook was "signum" (or sign) function.
right, and its value is either -1, 0, or 1 depending on the sign of its argument
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.
Oh, I see. Alright, thank you.