What is the limit as x approaches 0 of (sin(10x))/(11x) ?

The limit as x approaches 0 of (sin(10x))/(11x) is 10/11

Popular >

limit as x approaches 0 of (sin(10x))/(11x)

x \to 0 lim (\frac{sin ( 10 x )}{11 x})

\frac{10}{11}

Decimal

0.90909 \dots

Solution steps

x \to 0 lim (\frac{sin ( 10 x )}{11 x})

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

= \frac{1}{11} \cdot x \to 0 lim (\frac{sin ( 10 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 10 x ) \cdot 10}{1})

= \frac{1}{11} \cdot x \to 0 lim (\frac{cos ( 10 x ) \cdot 10}{1})

Plug in the value

x = 0

= \frac{1}{11} \cdot \frac{cos ( 10 \cdot 0 ) \cdot 10}{1}

Simplify

\frac{1}{11} \cdot \frac{cos ( 10 \cdot 0 ) \cdot 10}{1} : \frac{10}{11}

= \frac{10}{11}

\frac{\partial}{\partial y} (3 x y + y^{2})

y = e^{x} + x^{2}

\int \frac{5 e ^{x}}{e ^{2 x} + 2 e ^{x} + 1} d x

(- 4, 0), (1, - 5)

\frac{d}{d x} (x^{2} + 2 y^{2} - 4)

What is the limit as x approaches 0 of (sin(10x))/(11x) ?
The limit as x approaches 0 of (sin(10x))/(11x) is 10/11