What is the limit as t approaches 0 of (tan(3t))/t ?

The limit as t approaches 0 of (tan(3t))/t is 3

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limit as t approaches 0 of (tan(3t))/t

t \to 0 lim (\frac{tan ( 3 t )}{t})

3

Solution steps

t \to 0 lim (\frac{tan ( 3 t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{sec ^{2} ( 3 t ) \cdot 3}{1})

= t \to 0 lim (\frac{sec ^{2} ( 3 t ) \cdot 3}{1})

Plug in the value

t = 0

= \frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{sec ^{2} ( 3 \cdot 0 ) \cdot 3}{1} : 3

= 3

\frac{\partial}{\partial x} ((3 - x y) e^{- x y})

n = 1 \sum \infty (100) (\frac{1}{2})^{n}

- 1, 8, 4 e^{- 2 x} - 5

19 e^{x^{2}}

\frac{lo g _{e} ( x )}{x ^{2}}

What is the limit as t approaches 0 of (tan(3t))/t ?
The limit as t approaches 0 of (tan(3t))/t is 3