Limit chapter: Lim x--->(-pi/2)^- secx=?

Question

Would it be -inf ? not sure

Answer 1

as x goes to -pi/2 cosx approaches zero

secx= 1/cosx = 1/0

-secx approaches as a limit either - or + infinity. It's instead called "undefined"

did x approach -pi/2 from the less than or more than -pi/2.

if from Quadrant IV, then cosx is positive up until "reaching" (it never reaches) zero, and 1/cos approaches + infinity. But -1/cosx = 1/secx approaches negative infinity, so you're right if x approached -pi/2 in Quadrant IV.

if x approached -pi/2 from Quadrant III, then cosx approaches zero, but while negative, so 1/cosx = secx is negative infinity as a limit, and -secx approaches + infinity as a limit.

BUT maybe you meant by ^- that x approaches -pi/2 from the negative side and you were seeking the limit of secx, not the limit of -secx?

then approaching x=-pi/2 from the more negative x values, means approaching in Quadrant III, where cosx is negative and secx is negative. So then you're right, the limit is -inf. Unconditionally right.