Limit of sinØ over Ø as Ø approaches 0 is 1 I Limits of Trigonometric Function

Here's a summary of the provided video transcript, structured as requested, and translated into Volapük (as best as possible, given the limitations of accurately translating mathematical concepts and technical jargon into Volapük):

Short Summary:

Köt: Videogif älödob limät matematik, spesale fa funktions trigonometik, se sin(x)/x, if x läfob nulli.
Punktüls fa viktig: Videogif plädon metods fa kalkulön lims fa funktions trigonometik, gebon teorem sin(x)/x = 1 if x läfob nulli. Exempels gebons binons: lim sin(3x)/x, lim sin(7x)/sin(3x), lim sin(3x)/(x + tan(8x)).
Gebuns e konsekvens: Teorem at dünabon kalkulön lims fa funktions trigonometik kompleks, fa simplifizön expressions e gebon multiplikators fa „magik ün“.
Proseds e metods: Videogif demonön metods fa kalkulön lims fa multiplikön fa „ün“, faktörön, e gebon properties fa lims.

Detailed Summary:

Part 1: Lim fa sin(3x)/x: Videogif plädon teorem: lim sin(x)/x = 1 if x läfob nulli. To kalkulön lim sin(3x)/x, multiplikator (3/3 = 1) gebon, fa simplifizön expression ad 3 * lim sin(3x)/(3x) = 3 * 1 = 3. Metods fa simplifizön expressions e gebon teorem binons plädon in detail.
Part 2: Lim fa sin(7x)/sin(3x): Lim at kalkulön fa separön numerator e denominator, e multiplikön fa multiplikators fa „ün“ (7x/7x e 3x/3x). Teorem sin(x)/x = 1 gebon, fa simplifizön expression ad 7/3. Prosed at plädon in detail, fa demonön kanselizön fa faktors.
Part 3: Lim fa sin(3x)/(x + tan(8x)): Expression simplifizön fa konvertön tan(8x) ad sin(8x)/cos(8x). Multiplikator (cos(8x)/cos(8x) = 1) gebon. Expression simplifizön plu fa multiplikön fa multiplikators fa „ün“ (3x/3x e 8x/8x). Teorem sin(x)/x = 1 e properties fa lims gebons, fa resolön lim ad 1/3. Prosed at binon long e kompleks, ma demonön steps fa kalkulön in detail.
Part 4: Lim fa tan(6x)/sin(2x): Expression simplifizön fa konvertön tan(6x) ad sin(6x)/cos(6x). Multiplikators fa „ün“ gebons (6x/6x e 2x/2x). Teorem sin(x)/x = 1 e properties fa lims gebons, fa resolön lim ad 3. Prosed at binon plu kompleks, ma steps fa kalkulön plädon in detail.

Note: Accurate translation into Volapük of the mathematical expressions and detailed explanations is extremely challenging due to the limited mathematical vocabulary in Volapük. The above provides a reasonable approximation, focusing on conveying the overall meaning and structure. A fully accurate and technically precise translation would require a significant expansion of the Volapük lexicon.