Calculate the limit of \lim_{x \to 1} \frac{1-x^2}{\sin \pi x}

Carol Valentine

Carol Valentine

Answered question

2022-01-15

Calculate the limit of limx11x2sinπx only with the fundamental limits

Answer & Explanation

amarantha41

amarantha41

Beginner2022-01-16Added 38 answers

Let t=x−1. Then we have
1x2sin(πx)=t(t+2)sin(π(t+1))=t(t+2)sin(πt)
Now, set πt=y to find
limx11x2sin(πx)=limy0(ππ(yπ+2)ysiny)

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