Find the limit lim_{xrightarrow0}frac{xsin x}{2-2cos x}

Tazmin Horton 2020-10-28 Answered
Find the limit
limx0xsinx22cosx
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Expert Answer

likvau
Answered 2020-10-29 Author has 75 answers
To find the limit,
limx0xsinx22cosx
Let l=limx0xsinx22cosx
l=limx0xsinx2(1cosx)
l=limx0x(2sinx2cosx2)2(2sin2x2)   sinx=2sinx2cosx2, cosx=12sin2x2
l=limx0xcosx22sinx2
l=limx0x2sinx2limx0cosx2
l=limy0ysinycos0   let x2=y, then as x0,y0
l=limy01cosy (Applying LHospitals Rule)
l=1cos0
l=1
Therefore, limx0xsinx22cosx=1
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