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Advanced Math/Trigonometric limit.


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

Questioner:   Angelique
Country:   Gauteng, South Africa
Category:   Advanced Math
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)


 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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Paul Klarreich


I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.


I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.


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