What is the limit? lim x --> (pi/2), sec(x) - tan(x)
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What is the limit? lim x --> (pi/2), sec(x) - tan(x)

[From: ] [author: ] [Date: 11-12-20] [Hit: ]
......
   x→π/2

= lim cosx ̸ (1+sinx)
   x→π/2

= cos(π/2) ̸ (1+sin(π/2))

= 0 ̸ 2

= 0            ← ANSWER


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   lim sec(x) - tan(x)
   x→π/2

                                 (sec x + tan x)
   lim (sec x - tan x) ———————–
   x→π/2                   (sec x + tan x)


                        sec²x - tan²x
   lim ———————–———–
   x→π/2    (sec x + sec x·sin x)


                (tan²x + 1) - tan²x
   lim ———————–———–
   x→π/2    sec x(1 + sin x)


                                 1
   lim ———————–———–
   x→π/2         sec x(1 + sin x)



                          cos x                  cos(π/2)                0
   lim ———————–— = ———–——–— = ———–— = 0
   x→π/2         1 + sin x            1 + sin(π/2)            1 + 1



Have a good one!!
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