What is the limit as x approaches 0 of (tan(2x))/(5x) ?

The limit as x approaches 0 of (tan(2x))/(5x) is 2/5

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limit as x approaches 0 of (tan(2x))/(5x)

x \to 0 lim (\frac{tan ( 2 x )}{5 x})

\frac{2}{5}

Decimal

0.4

Solution steps

x \to 0 lim (\frac{tan ( 2 x )}{5 x})

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{2}{5}

\int \frac{4 sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

f (x) = x^{2} - \frac{1}{x}, at (- 1)

\int \frac{( 2 x + 7 )}{2 x ^{2} + 2 x + 1} d x

\int cos (2) x^{2} d x

f (x) = \frac{7}{x}, at x = 6

What is the limit as x approaches 0 of (tan(2x))/(5x) ?
The limit as x approaches 0 of (tan(2x))/(5x) is 2/5