limit as t approaches 0 of (sin(1-cos(t)))/(1-cos(t))

解答

t \to 0 lim (\frac{sin ( 1 - cos ( t ) )}{1 - cos ( t )})

1

求解步骤

t \to 0 lim (\frac{sin ( 1 - cos ( t ) )}{1 - cos ( t )})

使用洛必达法则

= t \to 0 lim (\frac{cos ( 1 - cos ( t ) ) sin ( t )}{sin ( t )})

约分:

sin (t)

= t \to 0 lim (cos (1 - cos (t)))

代入值

t = 0

= cos (1 - cos (0))

化简

cos (1 - cos (0)) : 1

= 1

x \to 0 lim (\frac{( 5 ^{x} - 6 ^{x} )}{x})

x \to - 7 + lim (f (x))

x \to - 9 lim (∣ x + 9 ∣)

h \to 1 lim (\frac{( 2 + h ) ^{2} - 4}{h})

x \to e lim (1)