What is the limit as t approaches 0 of (sin(1-cos(t)))/(1-cos(t)) ?

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Cancel the common factor:

sin (t)

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

Plug in the value

t = 0

= cos (1 - cos (0))

Simplify

cos (1 - cos (0)) : 1

= 1

x \to 1 lim (2 x - 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})

What is the limit as t approaches 0 of (sin(1-cos(t)))/(1-cos(t)) ?
The limit as t approaches 0 of (sin(1-cos(t)))/(1-cos(t)) is 1