Limit of a function as it tends to zerolimx→03(tan⁡2x)22x2What method is best for solving this? The division by zero is causing me issues when trying to apply Sandwich theorem and/or Algebra of limits.

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Drake Huang · Accepted Answer

I usually recommend to use basic results when dealing with simple limits. In this case here is my solution:limx→03(tan⁡2x)22x2=limx→03sin⁡2xsin⁡2x2x2cos⁡2xcos⁡2x=limx→0sin⁡2x2xsin⁡2x2x6cos22x=6,since sin⁡2x2x→1 and cos22x→1 when x goes to 0. To be more precise, if you put y=2x,x→0 implies y→0, solimx→0sin⁡2x2x=limy→0sin⁡yyand it is well known that this is 1. A similar trick can be applied to cos22x

Limit of a function as it tends to

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