limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)

解答

x \to 0 lim (\frac{5 + x - 5}{2 x})

\frac{1}{4 5}

十进制

0.11180 \dots

求解步骤

x \to 0 lim (\frac{5 + x - 5}{2 x})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{5 + x - 5}{x})

\frac{5 + x - 5}{x}

分子有理化:

\frac{1}{x + 5 + 5}

= \frac{1}{2} \cdot x \to 0 lim (\frac{1}{x + 5 + 5})

代入值

x = 0

= \frac{1}{2} \cdot \frac{1}{0 + 5 + 5}

化简

\frac{1}{2} \cdot \frac{1}{0 + 5 + 5} : \frac{1}{4 5}

= \frac{1}{4 5}

d er i v a t i v e f (t) = e^{7 t s i n (2 t)}

t an g e n t f (x) = x (27 x^{- 2} + 2), at x = - 3

\frac{\partial}{\partial x} (\frac{x - 1}{x + 1})

\int_{0}^{\infty} \frac{1}{e ^{x} - 1} d x

\frac{d}{d t} (\frac{1}{6} t^{3})