What is the limit as x approaches infinity of xsin((3pi)/x) ?

The limit as x approaches infinity of xsin((3pi)/x) is 3pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of xsin((3pi)/x)

x \to \infty lim (x sin (\frac{3 π}{x}))

3 π

Decimal Notation

9.42477 \dots

Solution steps

x \to \infty lim (x sin (\frac{3 π}{x}))

Rewrite for L'Hopital

= x \to \infty lim (\frac{sin ( \frac{3 π}{x} )}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to \infty lim \frac{- \frac{3 π c o s ( \frac{3 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

= x \to \infty lim \frac{- \frac{3 π c o s ( \frac{3 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

Simplify

\frac{- \frac{3 π c o s ( \frac{3 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}} : 3 π cos (\frac{3 π}{x})

= x \to \infty lim (3 π cos (\frac{3 π}{x}))

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

= 3 π \cdot x \to \infty lim (cos (\frac{3 π}{x}))

Apply the Limit Chain Rule:

1

= 3 π 1

Simplify

= 3 π

\int_{1}^{4} y ln (y) d y

\frac{d x}{d t} = k x (1000 - x)

y^{^{''}} + 400 y = sec (20 x), y (0) = 5, y^{^{'}} (0) = - 5

\int (x - 1) sec^{2} (x) d x

(x - 1) ln (x)

What is the limit as x approaches infinity of xsin((3pi)/x) ?
The limit as x approaches infinity of xsin((3pi)/x) is 3pi