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

y^{^{'}} = 6 e^{(2 x - y)}, y (0) = 0

\int \frac{( 1 + e ^{x} ) ^{2}}{e ^{x}} d x

y = 4 - x^{2}, y = 2 - x

\frac{d}{d x} (x csc (2 x))

\frac{1}{x} - \frac{2}{x ^{2}}

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