What is the limit as t approaches+0 of (2t)/(tan(t)) ?

The limit as t approaches+0 of (2t)/(tan(t)) is 2

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limit as t approaches+0 of (2t)/(tan(t))

t \to + 0 lim (\frac{2 t}{tan ( t )})

2

Solution steps

t \to 0 lim (\frac{2 t}{tan ( t )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= 2 \cdot t \to 0 lim (t cot (t))

Rewrite for L'Hopital

= 2 \cdot t \to 0 lim (\frac{t}{\frac{1}{c o t ( t )}})

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= 2

x \to \infty lim (- x - 1)

\int \frac{1}{9 x ^{2} + 16} d x

h \to 0 + lim (\frac{∣ h ∣}{h} + h^{2})

e^{f (x)}

2 x (1 - x)

What is the limit as t approaches+0 of (2t)/(tan(t)) ?
The limit as t approaches+0 of (2t)/(tan(t)) is 2