What is the limit as x approaches 0 of (cos(5x)tan(5x))/(3x) ?

The limit as x approaches 0 of (cos(5x)tan(5x))/(3x) is 5/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of (cos(5x)tan(5x))/(3x)

x \to 0 lim (\frac{cos ( 5 x ) tan ( 5 x )}{3 x})

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

x \to 0 lim (\frac{cos ( 5 x ) tan ( 5 x )}{3 x})

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

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 5 x ) tan ( 5 x )}{x})

cos (5 x) tan (5 x) = sin (5 x)

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( 5 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{1})

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{1})

Plug in the value

x = 0

= \frac{1}{3} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{1}{3} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1} : \frac{5}{3}

= \frac{5}{3}

\int - \frac{1}{( t + 2 ) ^{2}} d t

f (x) = x^{2} - x + 1

\frac{\partial}{\partial x} (13 x e^{y} - 11 y e^{- x})

\frac{\partial}{\partial x} (sin^{2} (a x))

\frac{\partial}{\partial y} (\frac{1}{x} + \frac{1}{y})

What is the limit as x approaches 0 of (cos(5x)tan(5x))/(3x) ?
The limit as x approaches 0 of (cos(5x)tan(5x))/(3x) is 5/3