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Question
lim x-0 1-cosx/sin(x/2)

Questioner:   Angelique
Country:   Gauteng, South Africa
Private:   No
Subject:   determine the limit if it exists
Question:   lim x-0 1-cosx/sin(x/2)
............................................
sin(x/2) = sqrt((1 - cos x)/2)  <<<<< basic identity

1-cos x/sin(x/2) =

1 - cos x
-------------------
sqrt((1 - cos x)/2)

Rationalize:

1 - cos x         sqrt((1 + cos x)/2)
------------------- ------------------
sqrt((1 - cos x)/2) sqrt((1 + cos x)/2)

(1 - cos x) sqrt((1 + cos x)/2)
-----------------------------------
sqrt((1 - cos^2 x)/4)

(1 - cos x) sqrt((1 + cos x)/2)
-----------------------------------
sqrt((sin^2 x)/4)

OK, take it from there.  Hint: You will have to do ANOTHER RATIONALIZING STEP.  iF YOU GET STUCK, SEND ME WHAT YOU DID.

Most of these limit problems involve:
1. Rationalizing a denomin/numer - ator.
2. Using one of those trig identities that you complained about having to memorize.

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