How to find : \lim_{x \to 1/4} \frac{1-\tan(\pi x)}{2x-\sqrt{x}}

Gage Potter

Gage Potter

Answered question

2022-04-20

How to find : limx141tan(πx)2xx

Answer & Explanation

Volsa280

Volsa280

Beginner2022-04-21Added 16 answers

limx141tanπx2xx=limx14tanπ4tanπx2xx×2x+x2x+x
=limx14sin(π4πx)cosπ4cosπx2x+x4x2x
=limx14sinπ(14x)cosπ4cosπx2x+x4x(14x)
=limx14sinπ(14x)π(14x)π4xcosπ4cosπx(2x+x)
=π2222(12+12)
=2π

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