What is the limit as θ approaches 0 of (tan(θ))/θ ?

The limit as θ approaches 0 of (tan(θ))/θ is 1

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limit as θ approaches 0 of (tan(θ))/θ

θ \to 0 lim (\frac{tan ( θ )}{θ})

1

Solution steps

θ \to 0 lim (\frac{tan ( θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{sec ^{2} ( θ )}{1})

= θ \to 0 lim (\frac{sec ^{2} ( θ )}{1})

Plug in the value

θ = 0

= \frac{sec ^{2} ( 0 )}{1}

Simplify

\frac{sec ^{2} ( 0 )}{1} : 1

= 1

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What is the limit as θ approaches 0 of (tan(θ))/θ ?
The limit as θ approaches 0 of (tan(θ))/θ is 1