What is the limit as x approaches 0 of 3xcsc(5x) ?

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

Popular >

limit as x approaches 0 of 3xcsc(5x)

x \to 0 lim (3 x csc (5 x))

\frac{3}{5}

Decimal Notation

0.6

Solution steps

x \to 0 lim (3 x csc (5 x))

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

= 3 \cdot x \to 0 lim (x csc (5 x))

Express with sin, cos

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{3}{5}

f (x) = cos (x) - 9 x

\frac{d}{d x} (sin (cos (sin (x))))

\frac{\partial}{\partial x} (\frac{c}{x})

\int 3 x^{2} - cos (x) + C d x

\int \frac{x}{202 1 ^{x}} d x

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