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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

= \frac{sin ( 0 )}{1}

Simplify

\frac{sin ( 0 )}{1} : 0

= 0

\frac{d}{d x} (4 cos (\frac{x}{2}))

y^{^{''}} - 3 y = 0

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

y^{^{''}} + 2 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

f (x) = x - 5 cos (x), at x = 0

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