limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h

解答

h \to 0 lim (\frac{cos ( \frac{π}{4} + h ) - cos ( \frac{π}{4} )}{h})

- \frac{2}{2}

十进制

- 0.70710 \dots

求解步骤

h \to 0 lim (\frac{cos ( \frac{π}{4} + h ) - cos ( \frac{π}{4} )}{h})

使用洛必达法则

= h \to 0 lim (\frac{- sin ( h + \frac{π}{4} )}{1})

代入值

h = 0

= \frac{- sin ( 0 + \frac{π}{4} )}{1}

化简

\frac{- sin ( 0 + \frac{π}{4} )}{1} : - \frac{2}{2}

= - \frac{2}{2}

x \to 0 lim ((1 - x) \frac{2}{x})

x \to 0 lim (\frac{e ^{x} - e ^{- x} - 2 ln ( 1 + x )}{x sin ( x )})

x \to 3 lim (\frac{x ^{2} + 3}{x - 3})

x \to 10 lim ((x - 10)^{10})

x \to 2 lim (x^{2} - 5 x + 4)