limit as x approaches pi/2+of 9/x sec(x)

解答

x \to \frac{π}{2} + lim (\frac{9}{x} sec (x))

- \infty

求解步骤

x \to \frac{π}{2} + lim (\frac{9}{x} sec (x))

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

= 9 \cdot x \to \frac{π}{2} + lim (\frac{1}{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)

不定型除外

= 9 \cdot x \to \frac{π}{2} + lim (\frac{1}{x}) \cdot x \to \frac{π}{2} + lim (sec (x))

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

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

= 9 \cdot \frac{2}{π} (- \infty)

运用无穷大属性:

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

= - \infty

\int \frac{5 ^{x}}{1 + 5 ^{x}} d x

im pl i c i t \frac{d y}{d x}, 16 x^{2} - 16 x y + y^{2} = 1

x \to 0 lim (x^{2} \cdot ln (x))

\int_{1}^{2} \frac{1}{x ^{2}} d x

x \to 0 + lim (x (ln (x)))