What is the limit as t approaches 0 of (t^2)/(1-cos^2(t)) ?

The limit as t approaches 0 of (t^2)/(1-cos^2(t)) is 1

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limit as t approaches 0 of (t^2)/(1-cos^2(t))

t \to 0 lim (\frac{t ^{2}}{1 - cos ^{2} ( t )})

1

Solution steps

t \to 0 lim (\frac{t ^{2}}{1 - cos ^{2} ( t )})

Apply L'Hopital's Rule

= t \to 0 lim (\frac{2 t}{sin ( 2 t )})

Apply L'Hopital's Rule

= t \to 0 lim (\frac{2}{cos ( 2 t ) \cdot 2})

Plug in the value

t = 0

= \frac{2}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{2}{cos ( 2 \cdot 0 ) \cdot 2} : 1

= 1

What is the limit as t approaches 0 of (t^2)/(1-cos^2(t)) ?
The limit as t approaches 0 of (t^2)/(1-cos^2(t)) is 1