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How would you prove this limit theorem? (1 Viewer)

Average Boreduser

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No u fucking retard ass bitch
u take - out from numerator, then u use double angle formula, take the 2 out and bobs your fucking uncle you dissappointment bitch
yeah I think this mans approach is pre good. you see the limit then turns to -2limsinx/x*limsinx and taking limx->0sinx=0 thererfore the rhs=0.
 

WeiWeiMan

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nah i think it is. its just noting limsinx/x=1 and limsinx=0. I think its basically what u said, but I think you'd lose marks if you don't indicate limfxgx=limfxlimgx
yeah prove that tho cuz i don't think it's explicitly stated in syllabus
 

cossine

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Why are you able to split the multiplication of the limits?
While other post have given answer I thought would add more detail. There things called indeterminant forms. Basically if you cannot evaluate a limit using substitution then you have indeterminant form. (E.g., 0/0, 0^0, infinity/infinity, 1^infinity, infinity - infinity, 0*infinity)

So in the question if we substitute theta = 0 in the question we will get 0/0 which is undefined.

In the case we have an indeterminant form then we can't apply the limit laws.

A simple example: lim x->infinity x - x. Applying the limit laws we would get infinity -infinity which is undefined. However by simplifying the expression we can see the limit is clearly 0. A minor note, don't confuse indeterminant forms with arithmetic. If you want ask a limit with indeterminant form infinity - infinity equals 0. But you shouldn't ask why does infinity -infinity equal 0.

Unfortunately, the proof of the limit laws going by memory involved epsilon delta definition of limits. For high school mathematics you are only expected to know the intuitive definition not the rigorous epsilon delta definition.

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/02:_Limits/2.03:_The_Limit_Laws
 

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