Предмет: Математика, автор: qwertyf

lim x стремится к бесконечности (x-5)sin(1/x-5)

Ответы

Автор ответа: HSS9860

Рассмотрите такое решение (неопределённость "бесконечность * ноль"):
$lim_{x \to \infty}(x-5)sin( \frac{1}{x-5})=lim_{x \to \infty}((x-5)* \frac{1}{x-5}* \frac{sin \frac{1}{x-5}}{ \frac{1}{x-5}})=1.$
Для "ухода" от синуса использован Первый замечательный.

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