limit as x approaches 1/2+of x^2tan(pix)

解

x \to \frac{1}{2} + lim (x^{2} tan (π x))

- \infty

解答ステップ

x \to \frac{1}{2} + lim (x^{2} tan (π x))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

不定形式の場合を除く

= x \to \frac{1}{2} + lim (x^{2}) \cdot x \to \frac{1}{2} + lim (tan (π x))

x \to \frac{1}{2} + lim (x^{2}) = \frac{1}{4}

x \to \frac{1}{2} + lim (tan (π x)) = - \infty

= \frac{1}{4} (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty