What is the limit as x approaches 0 of (5x)/(tan(x)) ?

The limit as x approaches 0 of (5x)/(tan(x)) is 5

limit as x approaches 0 of (5x)/(tan(x))

x \to 0 lim (\frac{5 x}{tan ( x )})

5

Solution steps

x \to 0 lim (\frac{5 x}{tan ( x )})

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

= 5 \cdot x \to 0 lim (\frac{x}{tan ( x )})

Use the basic trigonometric identity:

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

= 5 \cdot x \to 0 lim (x cot (x))

Rewrite for L'Hopital

= 5 \cdot x \to 0 lim (\frac{x}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

= 5 \cdot x \to 0 lim (\frac{1}{sec ^{2} ( x )})

Plug in the value

x = 0

= 5 \cdot \frac{1}{sec ^{2} ( 0 )}

Simplify

5 \cdot \frac{1}{sec ^{2} ( 0 )} : 5

= 5

\int 2 + tan^{2} (θ) d θ

\frac{d}{d x} (\frac{x ^{3}}{7})

\frac{\partial}{\partial x} (x y^{2} e^{- x z})

t a y l or arcsin (x)

y^{^{'}} + y = 5 cos (2 t), y (0) = 3

What is the limit as x approaches 0 of (5x)/(tan(x)) ?
The limit as x approaches 0 of (5x)/(tan(x)) is 5