Question

lim(4/(1-x^4))-(2/(1-x^2))=бесконечность делить на - бесконечность
x стремится к 1

Answer 1

Ответ:$lim_{x to 1}( frac{4 }{1-x^{4}} - frac{2}{1-x^{2}}) = lim_{x to 1}( frac{4 }{1-x^{4}} - frac{2(1+x^{2})}{(1-x^{2})(1+x^{2})}) = lim_{x to 1}( frac{4 }{1-x^{4}} - frac{2+2x^{2} }{1-x^{4}} ) = lim_{x to 1} frac{4-2-2x^{2}}{1-x^{4}} = lim_{x to 1} frac{2-2x^{2}}{1-x^{4}} =lim_{x to 1} frac{2(1-x^{2})}{(1-x^{2} )(1+x^{2})} = lim_{x to 1} frac{2 }{1+x^{2} } = 1$

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