limit as x approaches (7pi)/2+of xsec(x)

解

x \to \frac{7 π}{2} + lim (x sec (x))

\infty

解答ステップ

x \to \frac{7 π}{2} + lim (x sec (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{7 π}{2} + lim (x) \cdot x \to \frac{7 π}{2} + lim (sec (x))

x \to \frac{7 π}{2} + lim (x) = \frac{7 π}{2}

x \to \frac{7 π}{2} + lim (sec (x)) = \infty

= \frac{7 π}{2} \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty